Atkin-Lehner |
2+ 5+ 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
69440h |
Isogeny class |
Conductor |
69440 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
20480 |
Modular degree for the optimal curve |
Δ |
1111040 = 210 · 5 · 7 · 31 |
Discriminant |
Eigenvalues |
2+ 0 5+ 7+ 0 -6 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1448,-21208] |
[a1,a2,a3,a4,a6] |
Generators |
[122:1272:1] [554:13008:1] |
Generators of the group modulo torsion |
j |
327890958336/1085 |
j-invariant |
L |
9.0128106679598 |
L(r)(E,1)/r! |
Ω |
0.77394036942098 |
Real period |
R |
23.290710819772 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999934 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69440cp1 8680n1 |
Quadratic twists by: -4 8 |