Atkin-Lehner |
2- 19+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
12616d |
Isogeny class |
Conductor |
12616 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
25152 |
Modular degree for the optimal curve |
Δ |
-3998523517952 = -1 · 210 · 196 · 83 |
Discriminant |
Eigenvalues |
2- -1 0 1 5 -4 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-50168,-4309412] |
[a1,a2,a3,a4,a6] |
Generators |
[642642:27600616:343] |
Generators of the group modulo torsion |
j |
-13636809560150500/3904808123 |
j-invariant |
L |
3.8519566183606 |
L(r)(E,1)/r! |
Ω |
0.15949779394257 |
Real period |
R |
6.0376330655512 |
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 |
25232a1 100928f1 113544b1 |
Quadratic twists by: -4 8 -3 |