Atkin-Lehner |
2- 3- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
8112bd |
Isogeny class |
Conductor |
8112 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
19968 |
Modular degree for the optimal curve |
Δ |
-30071097298944 = -1 · 212 · 32 · 138 |
Discriminant |
Eigenvalues |
2- 3- -1 -2 2 13+ -7 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-27096,-1745964] |
[a1,a2,a3,a4,a6] |
Generators |
[732:19266:1] |
Generators of the group modulo torsion |
j |
-658489/9 |
j-invariant |
L |
4.58688577056 |
L(r)(E,1)/r! |
Ω |
0.18590403752511 |
Real period |
R |
2.0561171557577 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
507a1 32448cb1 24336bj1 8112ba1 |
Quadratic twists by: -4 8 -3 13 |