Atkin-Lehner |
2+ 11+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
33088f |
Isogeny class |
Conductor |
33088 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
30720 |
Modular degree for the optimal curve |
Δ |
-138781130752 = -1 · 228 · 11 · 47 |
Discriminant |
Eigenvalues |
2+ 2 2 1 11+ -1 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,703,16193] |
[a1,a2,a3,a4,a6] |
Generators |
[616:15291:1] |
Generators of the group modulo torsion |
j |
146363183/529408 |
j-invariant |
L |
9.487032413273 |
L(r)(E,1)/r! |
Ω |
0.73532497163198 |
Real period |
R |
6.4509113516285 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33088bl1 1034c1 |
Quadratic twists by: -4 8 |