Atkin-Lehner |
3+ 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
31713a |
Isogeny class |
Conductor |
31713 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
21360 |
Modular degree for the optimal curve |
Δ |
-40563812883 = -1 · 3 · 114 · 314 |
Discriminant |
Eigenvalues |
0 3+ -2 0 11+ 1 8 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,641,-7626] |
[a1,a2,a3,a4,a6] |
Generators |
[116:1270:1] |
Generators of the group modulo torsion |
j |
31490048/43923 |
j-invariant |
L |
3.0093867598758 |
L(r)(E,1)/r! |
Ω |
0.60978286158133 |
Real period |
R |
2.4675888332378 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
95139f1 31713g1 |
Quadratic twists by: -3 -31 |