Atkin-Lehner |
2+ 3- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
82368ba |
Isogeny class |
Conductor |
82368 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
599040 |
Modular degree for the optimal curve |
Δ |
-2462556006383616 = -1 · 231 · 36 · 112 · 13 |
Discriminant |
Eigenvalues |
2+ 3- -3 -5 11+ 13+ -7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,7476,-2374544] |
[a1,a2,a3,a4,a6] |
Generators |
[117:319:1] [174:2048:1] |
Generators of the group modulo torsion |
j |
241804367/12886016 |
j-invariant |
L |
7.1671913256931 |
L(r)(E,1)/r! |
Ω |
0.21912291033786 |
Real period |
R |
4.0885679837182 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000057 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
82368et1 2574p1 9152i1 |
Quadratic twists by: -4 8 -3 |