Atkin-Lehner |
2- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
75712cm |
Isogeny class |
Conductor |
75712 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
645120 |
Modular degree for the optimal curve |
Δ |
-17278801104388096 = -1 · 214 · 75 · 137 |
Discriminant |
Eigenvalues |
2- 0 -3 7- 2 13+ -4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-394784,-95683744] |
[a1,a2,a3,a4,a6] |
Generators |
[13585:1581671:1] |
Generators of the group modulo torsion |
j |
-86044336128/218491 |
j-invariant |
L |
4.4209566929647 |
L(r)(E,1)/r! |
Ω |
0.095216806512645 |
Real period |
R |
4.6430423927644 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000003497 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75712d1 18928v1 5824t1 |
Quadratic twists by: -4 8 13 |