Atkin-Lehner |
2- 29- 37- |
Signs for the Atkin-Lehner involutions |
Class |
68672bg |
Isogeny class |
Conductor |
68672 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
697944850432 = 214 · 292 · 373 |
Discriminant |
Eigenvalues |
2- 1 -4 -5 3 -2 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-8325,-292381] |
[a1,a2,a3,a4,a6] |
Generators |
[-50:37:1] [166:1711:1] |
Generators of the group modulo torsion |
j |
3895010796544/42599173 |
j-invariant |
L |
8.041931710503 |
L(r)(E,1)/r! |
Ω |
0.50013371212232 |
Real period |
R |
2.6799272259718 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000056 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68672n1 17168b1 |
Quadratic twists by: -4 8 |