Atkin-Lehner |
2- 3- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
66978n |
Isogeny class |
Conductor |
66978 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
1428480 |
Modular degree for the optimal curve |
Δ |
-82478142988535124 = -1 · 22 · 38 · 617 |
Discriminant |
Eigenvalues |
2- 3- -1 -1 -1 -5 2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-6865943,6926388995] |
[a1,a2,a3,a4,a6] |
Generators |
[40953:-13048:27] |
Generators of the group modulo torsion |
j |
-953054410321/2196 |
j-invariant |
L |
7.8392899342187 |
L(r)(E,1)/r! |
Ω |
0.29522126253971 |
Real period |
R |
1.6596217244798 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001008 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
22326e1 1098d1 |
Quadratic twists by: -3 61 |