Atkin-Lehner |
2- 7+ 11+ 41- |
Signs for the Atkin-Lehner involutions |
Class |
69454k |
Isogeny class |
Conductor |
69454 |
Conductor |
∏ cp |
44 |
Product of Tamagawa factors cp |
deg |
1138368 |
Modular degree for the optimal curve |
Δ |
-2838415487027642368 = -1 · 222 · 7 · 119 · 41 |
Discriminant |
Eigenvalues |
2- 2 0 7+ 11+ -4 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-97468,-81940451] |
[a1,a2,a3,a4,a6] |
Generators |
[16959:268355:27] |
Generators of the group modulo torsion |
j |
-43428615875/1203765248 |
j-invariant |
L |
13.458111094884 |
L(r)(E,1)/r! |
Ω |
0.11050765387071 |
Real period |
R |
2.7678278429877 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000024 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69454f1 |
Quadratic twists by: -11 |