Atkin-Lehner |
2- 7+ 19+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
61712g |
Isogeny class |
Conductor |
61712 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
1677312 |
Modular degree for the optimal curve |
Δ |
-1418643403289133056 = -1 · 226 · 74 · 192 · 293 |
Discriminant |
Eigenvalues |
2- 3 1 7+ -1 1 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1160827,-484791382] |
[a1,a2,a3,a4,a6] |
Generators |
[1341654:104027147:216] |
Generators of the group modulo torsion |
j |
-42234393984440290641/346348487131136 |
j-invariant |
L |
11.775905854289 |
L(r)(E,1)/r! |
Ω |
0.072688397637458 |
Real period |
R |
6.7502209413239 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000103 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7714f1 |
Quadratic twists by: -4 |