Atkin-Lehner |
2- 13- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
34112p |
Isogeny class |
Conductor |
34112 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
96768 |
Modular degree for the optimal curve |
Δ |
-123921785421824 = -1 · 225 · 133 · 412 |
Discriminant |
Eigenvalues |
2- 1 -1 1 -2 13- -5 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-108321,-13768609] |
[a1,a2,a3,a4,a6] |
Generators |
[2497:123656:1] |
Generators of the group modulo torsion |
j |
-536198730680521/472724096 |
j-invariant |
L |
5.741476544689 |
L(r)(E,1)/r! |
Ω |
0.13157340062833 |
Real period |
R |
3.6364217724797 |
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 |
34112d1 8528c1 |
Quadratic twists by: -4 8 |