Atkin-Lehner |
2- 3+ 5+ 13+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
57720r |
Isogeny class |
Conductor |
57720 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
239616 |
Modular degree for the optimal curve |
Δ |
-850713746688000 = -1 · 211 · 312 · 53 · 132 · 37 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -3 1 13+ -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,4144,1398156] |
[a1,a2,a3,a4,a6] |
Generators |
[10:9477:8] |
Generators of the group modulo torsion |
j |
3841918917982/415387571625 |
j-invariant |
L |
3.0547465287867 |
L(r)(E,1)/r! |
Ω |
0.38409924827117 |
Real period |
R |
1.9882533893632 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996031 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
115440w1 |
Quadratic twists by: -4 |