Atkin-Lehner |
2+ 3- 7+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
31584k |
Isogeny class |
Conductor |
31584 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-188070694644672 = -1 · 26 · 312 · 76 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 4 7+ -2 0 -6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-83286,-9302688] |
[a1,a2,a3,a4,a6] |
Generators |
[408:4980:1] |
Generators of the group modulo torsion |
j |
-998308954108593856/2938604603823 |
j-invariant |
L |
8.4308488113359 |
L(r)(E,1)/r! |
Ω |
0.14049134263554 |
Real period |
R |
5.0008115880889 |
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 |
31584f1 63168ch2 94752bb1 |
Quadratic twists by: -4 8 -3 |