Atkin-Lehner |
2+ 5+ 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
13640b |
Isogeny class |
Conductor |
13640 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
78720 |
Modular degree for the optimal curve |
Δ |
-403098446080000 = -1 · 211 · 54 · 11 · 315 |
Discriminant |
Eigenvalues |
2+ 0 5+ 3 11+ 0 5 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-468803,123551198] |
[a1,a2,a3,a4,a6] |
Generators |
[-26:11650:1] |
Generators of the group modulo torsion |
j |
-5563715398863351858/196825413125 |
j-invariant |
L |
4.7027421792243 |
L(r)(E,1)/r! |
Ω |
0.49821709478418 |
Real period |
R |
4.7195712757122 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
27280d1 109120n1 122760cd1 68200p1 |
Quadratic twists by: -4 8 -3 5 |