Curve detail

Definition

Name secp112r2
Category secg
Description A randomly generated curve. [SEC2v1](https://www.secg.org/SEC2-Ver-1.0.pdf) states 'E was chosen verifiably at random as specified in ANSI X9.62 [1] from the seed'.
Field Prime (0xdb7c2abf62e35e668076bead208b)
Field bits 112
Form Weierstrass $y^2 = x^3 + ax + b$
Param $a$ 0x6127c24c05f38a0aaaf65c0ef02c
Param $b$ 0x51def1815db5ed74fcc34c85d709
Generator $x$ 0x4ba30ab5e892b4e1649dd0928643
Generator $y$ 0xadcd46f5882e3747def36e956e97
Simulation seed 0x2757a1114d696e6768756151755316c05e0bd4

Characteristics

Order 0x36df0aafd8b8d7597ca10520d04b
Cofactor 0x4
$j$-invariant 0x597e254b44d77100b6eb01a0fecc
Trace $t$ 0x1008df2aa29df60
Embedding degree $k$ 0x124a58e5483d9d1dd435ac60456e
CM discriminant -0x9b351dbd00959c5113358ac3078b

Traits

$\text{cofactor}()$
order 0x36df0aafd8b8d7597ca10520d04b
cofactor 0x4
$\text{discriminant}()$
cm_disc -0x9b351dbd00959c5113358ac3078b
factorization ['0x2', '0x2', '0x17', '0x6bf86dbb21cc40386668077c8ad']
max_conductor 0x2
$\text{twist_order}(deg=1)$
twist_cardinality 0xdb7c2abf62e35f670e6968d6ffec
factorization None
$\text{twist_order}(deg=2)$
twist_cardinality 0xbc2dad5ce3bc2b4e238afa969c1823c49104f18fc477259ea64f2e64
factorization None
$\text{kn_factorization}(k=1)$
(+)factorization ['0x5', '0xa8353', '0x252a883ac97', '0x1cc2c5666f645']
(+)largest_factor_bitlen 0x31
(-)factorization NO DATA (timed out)
(-)largest_factor_bitlen -
$\text{kn_factorization}(k=2)$
(+)factorization ['0x3', '0x3', '0x236877f647c3b', '0x160a3819616d7b63']
(+)largest_factor_bitlen 0x3d
(-)factorization ['0xd', '0x35', '0xa36a66605', '0xff81acc4e7e3d811b']
(-)largest_factor_bitlen 0x44
$\text{kn_factorization}(k=3)$
(+)factorization ['0x101', '0x314b', '0x844ceaf', '0x19bf3b63a93482d41']
(+)largest_factor_bitlen 0x41
(-)factorization ['0x7', '0x25', '0x47', '0x768420a91', '0x13ccdcc4711ea5807']
(-)largest_factor_bitlen 0x41
$\text{kn_factorization}(k=4)$
(+)factorization ['0x7', '0x269', '0x47a8c5', '0xff14b7', '0xba92f7267dac75']
(+)largest_factor_bitlen 0x38
(-)factorization ['0x3', '0x5', '0xb', '0x67', '0xd3981aa1285645c3e83726045']
(-)largest_factor_bitlen 0x64
$\text{kn_factorization}(k=5)$
(+)factorization ['0x3', '0x1f73f', '0x8ff297', '0x14af0872a85de0a2387']
(+)largest_factor_bitlen 0x49
(-)factorization ['0x295', '0x599', '0x29cbb7', '0xbadd7577', '0x27d20c94b17']
(-)largest_factor_bitlen 0x2a
$\text{kn_factorization}(k=6)$
(+)factorization ['0x5', '0x1b12fe8d77a3', '0x9ba687d5e6c7b6047']
(+)largest_factor_bitlen 0x44
(-)factorization ['0x17', '0x17', '0xc5', '0x33c28ed360131bf6866dc2cab']
(-)largest_factor_bitlen 0x62
$\text{kn_factorization}(k=7)$
(+)factorization ['0xb', '0x11', '0x1f', '0x43d930aceba6c68996b41cc651']
(+)largest_factor_bitlen 0x67
(-)factorization ['0x3', '0x3', '0x3', '0x3', '0x4f', '0x5fb', '0x643fd', '0x1a3ed70231a7accc763']
(-)largest_factor_bitlen 0x49
$\text{kn_factorization}(k=8)$
(+)factorization ['0x3', '0xa793', '0x37e244c5dc895669d48a6d3e9']
(+)largest_factor_bitlen 0x62
(-)factorization ['0x136d', '0x5a63a08f0fdc5252a6e5ef047b']
(-)largest_factor_bitlen 0x67
$\text{torsion_extension}(l=2)$
least 0x1
full 0x2
relative 0x2
$\text{torsion_extension}(l=3)$
least 0x8
full 0x8
relative 0x1
$\text{torsion_extension}(l=5)$
least 0x18
full 0x18
relative 0x1
$\text{torsion_extension}(l=7)$
least 0x3
full 0x6
relative 0x2
$\text{torsion_extension}(l=11)$
least 0x5
full 0xa
relative 0x2
$\text{torsion_extension}(l=13)$
least 0x3
full 0xc
relative 0x4
$\text{torsion_extension}(l=17)$
least 0x120
full 0x120
relative 0x1
$\text{conductor}(deg=2)$
ratio_sqrt 0x1008df2aa29df60
factorization ['0x2', '0x2', '0x2', '0x2', '0x2', '0xb', '0xba95c7c192d1']
$\text{conductor}(deg=3)$
ratio_sqrt 0x25a0094a2653a9ef348e10fb4375
factorization ['0x2dc1f', '0xc0cef09fb', '0x1177def6a4b58d1']
$\text{conductor}(deg=4)$
ratio_sqrt 0xb640f816a3b00b073a02d59f17826031a816cf1240
factorization ['0x2', '0x2', '0x2', '0x2', '0x2', '0x2', '0x3', '0xb', '0xd', '0x3b', '0xba95c7c192d1', '0xa1dd2e942e564b66bb0d2d027']
$\text{embedding}()$
embedding_degree_complement 0x3
complement_bit_length 0x2
$\text{class_number}()$
upper 0x131df8ac6963e39a
lower 0x0
$\text{small_prime_order}(l=2)$
order None
complement_bit_length None
$\text{small_prime_order}(l=3)$
order 0x36df0aafd8b8d7597ca10520d04a
complement_bit_length 0x2
$\text{small_prime_order}(l=5)$
order 0x1b6f8557ec5c6bacbe5082906825
complement_bit_length 0x3
$\text{small_prime_order}(l=7)$
order 0x618c84c6d69df09f16739756c7a
complement_bit_length 0x5
$\text{small_prime_order}(l=11)$
order 0x36df0aafd8b8d7597ca10520d04a
complement_bit_length 0x2
$\text{small_prime_order}(l=13)$
order 0x36df0aafd8b8d7597ca10520d04a
complement_bit_length 0x2
$\text{division_polynomials}(l=2)$
factorization [['0x1', '0x1'], ['0x2', '0x1']]
len 0x2
$\text{division_polynomials}(l=3)$
factorization [['0x4', '0x1']]
len 0x1
$\text{division_polynomials}(l=5)$
factorization [['0xc', '0x1']]
len 0x1
$\text{volcano}(l=2)$
crater_degree 0x0
depth 0x1
$\text{volcano}(l=3)$
crater_degree 0x0
depth 0x0
$\text{volcano}(l=5)$
crater_degree 0x0
depth 0x0
$\text{volcano}(l=7)$
crater_degree 0x2
depth 0x0
$\text{volcano}(l=11)$
crater_degree 0x2
depth 0x0
$\text{volcano}(l=13)$
crater_degree 0x2
depth 0x0
$\text{volcano}(l=17)$
crater_degree 0x0
depth 0x0
$\text{volcano}(l=19)$
crater_degree 0x0
depth 0x0
$\text{isogeny_extension}(l=2)$
least 0x1
full 0x2
relative 0x2
$\text{isogeny_extension}(l=3)$
least 0x4
full 0x4
relative 0x1
$\text{isogeny_extension}(l=5)$
least 0x6
full 0x6
relative 0x1
$\text{isogeny_extension}(l=7)$
least 0x1
full 0x6
relative 0x6
$\text{isogeny_extension}(l=11)$
least 0x1
full 0x2
relative 0x2
$\text{isogeny_extension}(l=13)$
least 0x1
full 0x4
relative 0x4
$\text{isogeny_extension}(l=17)$
least 0x12
full 0x12
relative 0x1
$\text{isogeny_extension}(l=19)$
least 0x14
full 0x14
relative 0x1
$\text{trace_factorization}(deg=1)$
trace 0x1008df2aa29df60
trace_factorization ['0x2', '0x2', '0x2', '0x2', '0x2', '0xb', '0xba95c7c192d1']
number_of_factors 0x3
$\text{trace_factorization}(deg=2)$
trace 0x1008df2aa29df60
trace_factorization ['0x2', '0x3', '0xd', '0x3b', '0xa1dd2e942e564b66bb0d2d027']
number_of_factors 0x5
$\text{isogeny_neighbors}(l=2)$
len 0x1
$\text{isogeny_neighbors}(l=3)$
len 0x0
$\text{isogeny_neighbors}(l=5)$
len 0x0
$\text{q_torsion}()$
Q_torsion 0x1
$\text{hamming_x}(weight=1)$
x_coord_count 0x30
expected 0x38
ratio 1.16667
$\text{hamming_x}(weight=2)$
x_coord_count 0xc49
expected 0xc24
ratio 0.98824
$\text{hamming_x}(weight=3)$
x_coord_count 0x1bd45
expected 0x1bd28
ratio 0.99975
$\text{square_4p1}()$
p 0x1
order 0x1
$\text{pow_distance}()$
distance 0x2483d5409d1ca29a0d7beb7cbed4
ratio 6.01082
distance 32 0xc
distance 64 0x14
$\text{multiples_x}(k=1)$
Hx 0x4ba30ab5e892b4e1649dd0928643
bits 0x6f
difference 0x1
ratio 1.00909
$\text{multiples_x}(k=2)$
Hx 0x7beda5a3fa2430485f6af7358119
bits 0x6f
difference 0x1
ratio 1.00909
$\text{multiples_x}(k=3)$
Hx 0x8d6d9bdc3be62801b3bd313a4046
bits 0x70
difference 0x0
ratio 1.01818
$\text{multiples_x}(k=4)$
Hx 0x79537101c56a67185de36f3c4ec
bits 0x6b
difference 0x5
ratio 0.97273
$\text{multiples_x}(k=5)$
Hx 0x10d27920175e2c62072f56125270
bits 0x6d
difference 0x3
ratio 0.99091
$\text{multiples_x}(k=6)$
Hx 0x712478aabc6dd5beaddcaa2459b6
bits 0x6f
difference 0x1
ratio 1.00909
$\text{multiples_x}(k=7)$
Hx 0xbb30048f4364f01b3425a7386cce
bits 0x70
difference 0x0
ratio 1.01818
$\text{multiples_x}(k=8)$
Hx 0x2c8527a41a50bbad4cfe60502659
bits 0x6e
difference 0x2
ratio 1.0
$\text{multiples_x}(k=9)$
Hx 0x26c6dc30b0fd449eca64dc61cb9c
bits 0x6e
difference 0x2
ratio 1.0
$\text{multiples_x}(k=10)$
Hx 0x63bb286f484112be379ef42bc85d
bits 0x6f
difference 0x1
ratio 1.00909
$\text{x962_invariant}()$
r 0x560bc550e87218cb56e9f893eeca
$\text{brainpool_overlap}()$
o None
$\text{weierstrass}()$
a 0x6127c24c05f38a0aaaf65c0ef02c
b 0x51def1815db5ed74fcc34c85d709