Atkin-Lehner |
2- 7+ 19+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
61712h |
Isogeny class |
Conductor |
61712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
135168 |
Modular degree for the optimal curve |
Δ |
-1647317417984 = -1 · 216 · 74 · 192 · 29 |
Discriminant |
Eigenvalues |
2- 3 -1 7+ 3 -5 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3043,-89374] |
[a1,a2,a3,a4,a6] |
Generators |
[11541:236474:27] |
Generators of the group modulo torsion |
j |
-760798453689/402177104 |
j-invariant |
L |
10.588047239549 |
L(r)(E,1)/r! |
Ω |
0.31362057718019 |
Real period |
R |
4.2200863121562 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999811 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7714c1 |
Quadratic twists by: -4 |