Atkin-Lehner |
2+ 13- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
34112d |
Isogeny class |
Conductor |
34112 |
Conductor |
∏ cp |
24 |
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 |
[-365:2132:1] [25:3328:1] |
Generators of the group modulo torsion |
j |
-536198730680521/472724096 |
j-invariant |
L |
6.8840257598305 |
L(r)(E,1)/r! |
Ω |
0.58391315561666 |
Real period |
R |
0.49122785452011 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999988 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
34112p1 1066a1 |
Quadratic twists by: -4 8 |