Atkin-Lehner |
2- 3+ 11+ 59- |
Signs for the Atkin-Lehner involutions |
Class |
31152m |
Isogeny class |
Conductor |
31152 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
419328 |
Modular degree for the optimal curve |
Δ |
708151560946384896 = 216 · 314 · 11 · 593 |
Discriminant |
Eigenvalues |
2- 3+ 2 2 11+ -2 4 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-799712,272536320] |
[a1,a2,a3,a4,a6] |
Generators |
[12720:9440:27] |
Generators of the group modulo torsion |
j |
13809092721694064353/172888564684176 |
j-invariant |
L |
5.6769931005523 |
L(r)(E,1)/r! |
Ω |
0.28679925158356 |
Real period |
R |
3.2990515544739 |
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 |
3894p1 124608dh1 93456bs1 |
Quadratic twists by: -4 8 -3 |