Atkin-Lehner |
2- 3- 7+ 19+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
69426bk |
Isogeny class |
Conductor |
69426 |
Conductor |
∏ cp |
224 |
Product of Tamagawa factors cp |
deg |
1204224 |
Modular degree for the optimal curve |
Δ |
-427956970671046656 = -1 · 228 · 310 · 72 · 19 · 29 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ -6 0 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-335696,81294131] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:9073:1] [-1354:93017:8] |
Generators of the group modulo torsion |
j |
-5738963600386312633/587046599000064 |
j-invariant |
L |
12.977764709017 |
L(r)(E,1)/r! |
Ω |
0.2906042223053 |
Real period |
R |
0.79746191069775 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999522 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23142j1 |
Quadratic twists by: -3 |