Atkin-Lehner |
2+ 3+ 11+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
15312b |
Isogeny class |
Conductor |
15312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
26027578672128 = 210 · 33 · 113 · 294 |
Discriminant |
Eigenvalues |
2+ 3+ 4 -2 11+ -4 6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-9736,279808] |
[a1,a2,a3,a4,a6] |
Generators |
[-18:670:1] |
Generators of the group modulo torsion |
j |
99680465505316/25417557297 |
j-invariant |
L |
5.0709676466188 |
L(r)(E,1)/r! |
Ω |
0.62680392192125 |
Real period |
R |
4.0450988493144 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7656i1 61248cp1 45936u1 |
Quadratic twists by: -4 8 -3 |