Atkin-Lehner |
3+ 5+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69825n |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2211840 |
Modular degree for the optimal curve |
Δ |
1415134792353515625 = 33 · 510 · 710 · 19 |
Discriminant |
Eigenvalues |
1 3+ 5+ 7- 0 2 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-8202625,-9045506000] |
[a1,a2,a3,a4,a6] |
Generators |
[-1111128287763211204933116:725714793130568655940934:673780890886158334609] |
Generators of the group modulo torsion |
j |
33202753467020929/769820625 |
j-invariant |
L |
6.6859288485661 |
L(r)(E,1)/r! |
Ω |
0.089209670979186 |
Real period |
R |
37.473116852931 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999978119 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
13965y1 9975i1 |
Quadratic twists by: 5 -7 |