Atkin-Lehner |
2- 3+ 5+ 7+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
87360ed |
Isogeny class |
Conductor |
87360 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
1161216 |
Modular degree for the optimal curve |
Δ |
144172269291960000 = 26 · 314 · 54 · 73 · 133 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7+ 0 13- 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-986536,-376381610] |
[a1,a2,a3,a4,a6] |
Generators |
[465994:112449675:8] |
Generators of the group modulo torsion |
j |
1659139840046304225856/2252691707686875 |
j-invariant |
L |
4.112789589398 |
L(r)(E,1)/r! |
Ω |
0.15149792819215 |
Real period |
R |
9.0491657393009 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000012847 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
87360gf1 43680ca2 |
Quadratic twists by: -4 8 |