Atkin-Lehner |
3+ 5+ 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69825p |
Isogeny class |
Conductor |
69825 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
811008 |
Modular degree for the optimal curve |
Δ |
-286510931396484375 = -1 · 3 · 514 · 77 · 19 |
Discriminant |
Eigenvalues |
1 3+ 5+ 7- 4 -2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-245025,-53418000] |
[a1,a2,a3,a4,a6] |
Generators |
[768846493166181266320:-164212210551700445086285:16931829209698304] |
Generators of the group modulo torsion |
j |
-885012508801/155859375 |
j-invariant |
L |
6.1356250482991 |
L(r)(E,1)/r! |
Ω |
0.10627168767895 |
Real period |
R |
28.8676372001 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999986678 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
13965s1 9975o1 |
Quadratic twists by: 5 -7 |