Curve detail

Definition

Name sect113r1 (secg/sect113r1, wtls/wap-wsg-idm-ecid-wtls4)
Category secg
Field Binary
Field polynomial $x^{113} + x^{9} + 1$
Field bits 113
Form Weierstrass $y^2 = x^3 + ax + b$
Param $a$ 0x003088250ca6e7c7fe649ce85820f7
Param $b$ 0x00e8bee4d3e2260744188be0e9c723
Generator $x$ 0x009d73616f35f4ab1407d73562c10f
Generator $y$ 0x00a52830277958ee84d1315ed31886

Characteristics

Order 0x100000000000000d9ccec8a39e56f
Cofactor 0x2
$j$-invariant 0x6942e38fc45c62366c09aa8204cd
Trace $t$ -0x1b399d91473cadd

Traits

$\text{cofactor}()$
order 0x100000000000000d9ccec8a39e56f
cofactor 0x2
$\text{discriminant}()$
cm_disc -0x51acbcbcf4bf67e859f4394b07d37
factorization ['0x7', '0x2f', '0x18892f79', '0x297162885b62c9ed33b7']
max_conductor 0x1
$\text{twist_order}(deg=1)$
twist_cardinality 0x1fffffffffffffe4c6626eb8c3524
factorization None
$\text{twist_order}(deg=2)$
twist_cardinality 0x3fffffffffffffffffffffffffffee5343430b409817a60bc6b4f82ca
factorization None
$\text{kn_factorization}(k=1)$
(+)factorization ['0x202c829afb', '0xfe9dd7c4efe1a3e0a6d']
(+)largest_factor_bitlen 0x4c
(-)factorization ['0x3', '0x5', '0x4e49b60ac13b01', '0x6f9d860de0b953']
(-)largest_factor_bitlen 0x37
$\text{kn_factorization}(k=2)$
(+)factorization ['0x3', '0x3', '0x3', '0x3', '0xd', '0x1d', '0x1f', '0xf711e1ef5', '0x49741371fbfb37f']
(+)largest_factor_bitlen 0x3b
(-)factorization ['0x241', '0xab695', '0xc00e3', '0x3886f9bfc2e1611a5']
(-)largest_factor_bitlen 0x42
$\text{kn_factorization}(k=3)$
(+)factorization ['0x7', '0xb', '0x963d', '0xa9b3b', '0x33469fe38250f72df09']
(+)largest_factor_bitlen 0x4a
(-)factorization ['0x11', '0x16f74b', '0x10e0911', '0x3bacf0627c4b64dcb']
(-)largest_factor_bitlen 0x42
$\text{kn_factorization}(k=4)$
(+)factorization ['0x5', '0x5', '0x5', '0x5', '0x346dc5d6388659778ff57602d89']
(+)largest_factor_bitlen 0x6a
(-)factorization ['0x3', '0x7', '0x7', '0x25', '0x2f', '0x2fca7', '0x6601e14c9', '0x1b9241934099']
(-)largest_factor_bitlen 0x2d
$\text{kn_factorization}(k=5)$
(+)factorization ['0x3', '0x18d', '0x14615', '0x1afff5e53efb467cf2108cd']
(+)largest_factor_bitlen 0x59
(-)factorization ['0x65', '0x2a1', '0x9a437b986df1658c6e3e5ea91']
(-)largest_factor_bitlen 0x64
$\text{kn_factorization}(k=6)$
(+)factorization ['0x3b', '0x59', '0x34c9', '0x293f9479', '0x119bf7359cd164e7']
(+)largest_factor_bitlen 0x3d
(-)factorization ['0x5', '0x10d', '0x248b532d1bfaabcda0c63722573']
(-)largest_factor_bitlen 0x6a
$\text{kn_factorization}(k=7)$
(+)factorization ['0x757', '0x29093', '0xbe6313729a2147f407b1e7']
(+)largest_factor_bitlen 0x58
(-)factorization ['0x3', '0x3', '0x1849', '0xdd6efd', '0x2607e3eb1', '0x7f9c362ba65']
(-)largest_factor_bitlen 0x2b
$\text{kn_factorization}(k=8)$
(+)factorization ['0x3', '0x4f', '0x5db', '0xfe9', '0xd802a401', '0x3848920b456877']
(+)largest_factor_bitlen 0x36
(-)factorization ['0xb', '0x17', '0x29b615d', '0x96e02b5ca5', '0xa898866430b']
(-)largest_factor_bitlen 0x2c
$\text{torsion_extension}(l=2)$
least None
full None
relative None
$\text{torsion_extension}(l=3)$
least 0x8
full 0x8
relative 0x1
$\text{torsion_extension}(l=5)$
least 0x2
full 0x4
relative 0x2
$\text{torsion_extension}(l=7)$
least 0x6
full 0x7
relative 0x1
$\text{torsion_extension}(l=11)$
least 0x2
full 0xa
relative 0x5
$\text{torsion_extension}(l=13)$
least 0x3
full 0xc
relative 0x4
$\text{torsion_extension}(l=17)$
least 0x2
full 0x8
relative 0x4
$\text{conductor}(deg=2)$
ratio_sqrt 0x1b399d91473cadd
factorization ['0x159f0cb', '0x1425985f7']
$\text{conductor}(deg=3)$
ratio_sqrt 0xe5343430b409817a60bc6b4f82c9
factorization ['0x46f9', '0x1d7c94a507e9', '0x1c09b46090aa29']
$\text{conductor}(deg=4)$
ratio_sqrt 0x1e1323eeb649088636ba0cb6623c4e4685a2ade7e7b
factorization ['0x3', '0x5', '0x2b', '0x611', '0x349d', '0x120e9', '0x159f0cb', '0x32ab69bf', '0x1425985f7', '0x193077a01']
$\text{embedding}()$
embedding_degree_complement 0x2
complement_bit_length 0x2
$\text{class_number}()$
upper 0x3900ee93cb8f66b7
lower 0x9ab
$\text{small_prime_order}(l=2)$
order None
complement_bit_length None
$\text{small_prime_order}(l=3)$
order 0x800000000000006ce676451cf2b7
complement_bit_length 0x2
$\text{small_prime_order}(l=5)$
order 0x100000000000000d9ccec8a39e56e
complement_bit_length 0x1
$\text{small_prime_order}(l=7)$
order 0x100000000000000d9ccec8a39e56e
complement_bit_length 0x1
$\text{small_prime_order}(l=11)$
order 0x100000000000000d9ccec8a39e56e
complement_bit_length 0x1
$\text{small_prime_order}(l=13)$
order 0x800000000000006ce676451cf2b7
complement_bit_length 0x2
$\text{division_polynomials}(l=2)$
factorization [['0x1', '0x2']]
len 0x1
$\text{division_polynomials}(l=3)$
factorization [['0x4', '0x1']]
len 0x1
$\text{division_polynomials}(l=5)$
factorization [['0x1', '0x2'], ['0x2', '0x1'], ['0x4', '0x2']]
len 0x3
$\text{volcano}(l=2)$
crater_degree 0x2
depth 0x0
$\text{volcano}(l=3)$
crater_degree 0x0
depth 0x0
$\text{volcano}(l=5)$
crater_degree 0x2
depth 0x0
$\text{volcano}(l=7)$
crater_degree 0x1
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 0x2
depth 0x0
$\text{volcano}(l=19)$
crater_degree 0x0
depth 0x0
$\text{isogeny_extension}(l=2)$
least None
full None
relative None
$\text{isogeny_extension}(l=3)$
least 0x4
full 0x4
relative 0x1
$\text{isogeny_extension}(l=5)$
least 0x1
full 0x4
relative 0x4
$\text{isogeny_extension}(l=7)$
least 0x1
full 0x7
relative 0x7
$\text{isogeny_extension}(l=11)$
least 0x1
full 0xa
relative 0xa
$\text{isogeny_extension}(l=13)$
least 0x1
full 0xc
relative 0xc
$\text{isogeny_extension}(l=17)$
least 0x1
full 0x8
relative 0x8
$\text{isogeny_extension}(l=19)$
least 0x14
full 0x14
relative 0x1
$\text{trace_factorization}(deg=1)$
trace -0x1b399d91473cadd
trace_factorization ['0x159f0cb', '0x1425985f7']
number_of_factors 0x2
$\text{trace_factorization}(deg=2)$
trace -0x1b399d91473cadd
trace_factorization ['0x3', '0x5', '0x2b', '0x611', '0x349d', '0x120e9', '0x32ab69bf', '0x193077a01']
number_of_factors 0x8
$\text{isogeny_neighbors}(l=2)$
len 0x3
$\text{isogeny_neighbors}(l=3)$
len 0x0
$\text{isogeny_neighbors}(l=5)$
len 0x2
$\text{q_torsion}()$
Q_torsion 0x1
$\text{hamming_x}(weight=1)$
x_coord_count 0x71
expected 0x39
ratio 0.50442
$\text{hamming_x}(weight=2)$
x_coord_count 0x18b8
expected 0xc94
ratio 0.50885
$\text{hamming_x}(weight=3)$
x_coord_count 0x39298
expected 0x1d5a8
ratio 0.51351
$\text{square_4p1}()$
p 0x1
order 0x1
$\text{pow_distance}()$
distance 0x1b399d91473cade
ratio 8.469560631090237e+16
distance 32 0x2
distance 64 0x1e
$\text{multiples_x}(k=1)$
Hx None
bits None
difference None
ratio None
$\text{multiples_x}(k=2)$
Hx None
bits None
difference None
ratio None
$\text{multiples_x}(k=3)$
Hx None
bits None
difference None
ratio None
$\text{multiples_x}(k=4)$
Hx None
bits None
difference None
ratio None
$\text{multiples_x}(k=5)$
Hx None
bits None
difference None
ratio None
$\text{multiples_x}(k=6)$
Hx None
bits None
difference None
ratio None
$\text{multiples_x}(k=7)$
Hx None
bits None
difference None
ratio None
$\text{multiples_x}(k=8)$
Hx None
bits None
difference None
ratio None
$\text{multiples_x}(k=9)$
Hx None
bits None
difference None
ratio None
$\text{multiples_x}(k=10)$
Hx None
bits None
difference None
ratio None
$\text{x962_invariant}()$
r 0x0
$\text{brainpool_overlap}()$
o None
$\text{weierstrass}()$
a None
b None