Atkin-Lehner |
2+ 3- 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
67032bh |
Isogeny class |
Conductor |
67032 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
294912 |
Modular degree for the optimal curve |
Δ |
133050012700752 = 24 · 312 · 77 · 19 |
Discriminant |
Eigenvalues |
2+ 3- -4 7- -4 -2 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-15582,-502495] |
[a1,a2,a3,a4,a6] |
Generators |
[-83:468:1] [-56:441:1] |
Generators of the group modulo torsion |
j |
304900096/96957 |
j-invariant |
L |
7.7061262478877 |
L(r)(E,1)/r! |
Ω |
0.43803552440298 |
Real period |
R |
2.1990585861655 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000022 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
22344bb1 9576h1 |
Quadratic twists by: -3 -7 |