Atkin-Lehner |
2+ 3- 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
15624k |
Isogeny class |
Conductor |
15624 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
199680 |
Modular degree for the optimal curve |
Δ |
-1570482043959580416 = -1 · 28 · 36 · 710 · 313 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ -2 -4 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-112311,62010090] |
[a1,a2,a3,a4,a6] |
Generators |
[-453:4464:1] |
Generators of the group modulo torsion |
j |
-839504640199248/8415220142959 |
j-invariant |
L |
3.50249465745 |
L(r)(E,1)/r! |
Ω |
0.22809144209426 |
Real period |
R |
2.5592766840141 |
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 |
31248s1 124992bz1 1736b1 109368n1 |
Quadratic twists by: -4 8 -3 -7 |