Atkin-Lehner |
2- 3+ 23+ 71- |
Signs for the Atkin-Lehner involutions |
Class |
39192g |
Isogeny class |
Conductor |
39192 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
566272 |
Modular degree for the optimal curve |
Δ |
194558317783645392 = 24 · 37 · 238 · 71 |
Discriminant |
Eigenvalues |
2- 3+ -2 -4 4 6 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-145039,-1235912] |
[a1,a2,a3,a4,a6] |
Generators |
[-2786224374939:164648199700831:95632080517] |
Generators of the group modulo torsion |
j |
21089248978550536192/12159894861477837 |
j-invariant |
L |
4.320556046505 |
L(r)(E,1)/r! |
Ω |
0.2666447372871 |
Real period |
R |
16.203417665252 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
78384i1 117576f1 |
Quadratic twists by: -4 -3 |