Atkin-Lehner |
2- 3+ 5+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
69360cl |
Isogeny class |
Conductor |
69360 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
497664 |
Modular degree for the optimal curve |
Δ |
22725879685632000 = 212 · 312 · 53 · 174 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -2 3 -4 17- -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-70901,-420099] |
[a1,a2,a3,a4,a6] |
Generators |
[-326:12393:8] |
Generators of the group modulo torsion |
j |
115220905984/66430125 |
j-invariant |
L |
3.521855916818 |
L(r)(E,1)/r! |
Ω |
0.31886369864423 |
Real period |
R |
1.840836660361 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000234 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4335e1 69360ds1 |
Quadratic twists by: -4 17 |