Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312bx |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-4633831094976 = -1 · 26 · 34 · 197 |
Discriminant |
Eigenvalues |
2+ 3- -3 3 -3 0 1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-103727,12824271] |
[a1,a2,a3,a4,a6] |
Generators |
[310:3249:1] |
Generators of the group modulo torsion |
j |
-40992251392/1539 |
j-invariant |
L |
6.5693362018703 |
L(r)(E,1)/r! |
Ω |
0.72391129063644 |
Real period |
R |
0.56717379311787 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000628 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312x1 34656k1 3648e1 |
Quadratic twists by: -4 8 -19 |