Atkin-Lehner |
2- 7+ 11- 41- |
Signs for the Atkin-Lehner involutions |
Class |
69454s |
Isogeny class |
Conductor |
69454 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
-18677014048 = -1 · 25 · 76 · 112 · 41 |
Discriminant |
Eigenvalues |
2- -2 0 7+ 11- -5 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,267,-6335] |
[a1,a2,a3,a4,a6] |
Generators |
[48:319:1] [30:155:1] |
Generators of the group modulo torsion |
j |
17392838375/154355488 |
j-invariant |
L |
10.561280896752 |
L(r)(E,1)/r! |
Ω |
0.60563135925092 |
Real period |
R |
1.7438464398195 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000023 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69454i1 |
Quadratic twists by: -11 |