Atkin-Lehner |
7- 29- 61- |
Signs for the Atkin-Lehner involutions |
Class |
86681h |
Isogeny class |
Conductor |
86681 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1997568 |
Modular degree for the optimal curve |
Δ |
-243554653021585843 = -1 · 715 · 292 · 61 |
Discriminant |
Eigenvalues |
0 0 -2 7- -4 -2 -3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-18027296,29460773095] |
[a1,a2,a3,a4,a6] |
Generators |
[1729:58824:1] [2419:2769:1] |
Generators of the group modulo torsion |
j |
-5507154254490173964288/2070180392707 |
j-invariant |
L |
6.9145493664772 |
L(r)(E,1)/r! |
Ω |
0.25306399058044 |
Real period |
R |
3.4154154798114 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999809 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12383d1 |
Quadratic twists by: -7 |