Atkin-Lehner |
2- 3+ 5+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
31200be |
Isogeny class |
Conductor |
31200 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
24576 |
Modular degree for the optimal curve |
Δ |
38025000000 = 26 · 32 · 58 · 132 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 0 -4 13+ -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1158,12312] |
[a1,a2,a3,a4,a6] |
Generators |
[-37:56:1] [-12:156:1] |
Generators of the group modulo torsion |
j |
171879616/38025 |
j-invariant |
L |
7.1705730217675 |
L(r)(E,1)/r! |
Ω |
1.0877683071982 |
Real period |
R |
3.296001995239 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
31200bu1 62400gz2 93600t1 6240m1 |
Quadratic twists by: -4 8 -3 5 |