Atkin-Lehner |
2- 3+ 37- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
31302j |
Isogeny class |
Conductor |
31302 |
Conductor |
∏ cp |
120 |
Product of Tamagawa factors cp |
deg |
432000 |
Modular degree for the optimal curve |
Δ |
49135370583932928 = 220 · 39 · 373 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 0 0 -4 2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1348355,-602203517] |
[a1,a2,a3,a4,a6] |
Generators |
[3211:166226:1] |
Generators of the group modulo torsion |
j |
13773517575474796875/2496335446016 |
j-invariant |
L |
8.3668518756446 |
L(r)(E,1)/r! |
Ω |
0.14010487295136 |
Real period |
R |
1.9906164335791 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
31302a1 |
Quadratic twists by: -3 |