Atkin-Lehner |
2+ 7- 17- 53- |
Signs for the Atkin-Lehner involutions |
Class |
12614d |
Isogeny class |
Conductor |
12614 |
Conductor |
∏ cp |
10 |
Product of Tamagawa factors cp |
deg |
20160 |
Modular degree for the optimal curve |
Δ |
242289712 = 24 · 75 · 17 · 53 |
Discriminant |
Eigenvalues |
2+ -3 -2 7- -3 2 17- -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-3703,87661] |
[a1,a2,a3,a4,a6] |
Generators |
[-35:434:1] [14:189:1] |
Generators of the group modulo torsion |
j |
5616306719736777/242289712 |
j-invariant |
L |
2.9520238548529 |
L(r)(E,1)/r! |
Ω |
1.6518527621725 |
Real period |
R |
0.17870986582182 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
100912o1 113526bc1 88298i1 |
Quadratic twists by: -4 -3 -7 |