Atkin-Lehner |
2+ 3+ 5- 11- |
Signs for the Atkin-Lehner involutions |
Class |
31680f |
Isogeny class |
Conductor |
31680 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
7785676800 = 220 · 33 · 52 · 11 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 0 11- 0 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-972,10864] |
[a1,a2,a3,a4,a6] |
Generators |
[8:60:1] |
Generators of the group modulo torsion |
j |
14348907/1100 |
j-invariant |
L |
6.0065984325448 |
L(r)(E,1)/r! |
Ω |
1.2875834586122 |
Real period |
R |
1.1662541935377 |
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 |
31680ce1 990a1 31680a1 |
Quadratic twists by: -4 8 -3 |