Atkin-Lehner |
3- 7- 11+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
61677l |
Isogeny class |
Conductor |
61677 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
878592 |
Modular degree for the optimal curve |
Δ |
-36730052779729617 = -1 · 317 · 74 · 113 · 89 |
Discriminant |
Eigenvalues |
1 3- 2 7- 11+ -7 1 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-865656,-309923955] |
[a1,a2,a3,a4,a6] |
j |
-98408473838096881537/50384160191673 |
j-invariant |
L |
2.5042047826641 |
L(r)(E,1)/r! |
Ω |
0.078256399518843 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
20559h1 |
Quadratic twists by: -3 |