Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696di |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
230400 |
Modular degree for the optimal curve |
Δ |
-232753523245056 = -1 · 214 · 36 · 117 |
Discriminant |
Eigenvalues |
2+ 3- -3 -2 11- -4 6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,11616,-553696] |
[a1,a2,a3,a4,a6] |
Generators |
[737:20207:1] |
Generators of the group modulo torsion |
j |
8192/11 |
j-invariant |
L |
4.3742883442944 |
L(r)(E,1)/r! |
Ω |
0.29713533374565 |
Real period |
R |
3.6803838585396 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995826 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69696gv1 4356h1 7744h1 6336r1 |
Quadratic twists by: -4 8 -3 -11 |