Atkin-Lehner |
2+ 3- 5- 11+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
28710p |
Isogeny class |
Conductor |
28710 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
69888 |
Modular degree for the optimal curve |
Δ |
-3488265000000 = -1 · 26 · 37 · 57 · 11 · 29 |
Discriminant |
Eigenvalues |
2+ 3- 5- -4 11+ -3 -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-4374,144180] |
[a1,a2,a3,a4,a6] |
Generators |
[36:-198:1] [-44:522:1] |
Generators of the group modulo torsion |
j |
-12696627240289/4785000000 |
j-invariant |
L |
5.9633290303605 |
L(r)(E,1)/r! |
Ω |
0.74413075230083 |
Real period |
R |
0.14310390757277 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999984 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
9570bb1 |
Quadratic twists by: -3 |