Atkin-Lehner |
2+ 3+ 5- 31- |
Signs for the Atkin-Lehner involutions |
Class |
115320g |
Isogeny class |
Conductor |
115320 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
3317760 |
Modular degree for the optimal curve |
Δ |
-3961816431984000000 = -1 · 210 · 32 · 56 · 317 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 4 -6 6 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-230960,104939100] |
[a1,a2,a3,a4,a6] |
Generators |
[170:8400:1] |
Generators of the group modulo torsion |
j |
-1499221444/4359375 |
j-invariant |
L |
7.3542641714571 |
L(r)(E,1)/r! |
Ω |
0.2179931120252 |
Real period |
R |
2.8113518719447 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000006622 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
3720e1 |
Quadratic twists by: -31 |