Atkin-Lehner |
2- 13- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
12688f |
Isogeny class |
Conductor |
12688 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
1344 |
Modular degree for the optimal curve |
Δ |
164944 = 24 · 132 · 61 |
Discriminant |
Eigenvalues |
2- 0 -2 -4 -4 13- -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-16,15] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:6:1] |
Generators of the group modulo torsion |
j |
28311552/10309 |
j-invariant |
L |
2.5998491192637 |
L(r)(E,1)/r! |
Ω |
2.9539194336513 |
Real period |
R |
1.7602708385652 |
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 |
3172b1 50752i1 114192bv1 |
Quadratic twists by: -4 8 -3 |