Atkin-Lehner |
2- 7+ 13+ 29- |
Signs for the Atkin-Lehner involutions |
Class |
68614s |
Isogeny class |
Conductor |
68614 |
Conductor |
∏ cp |
9 |
Product of Tamagawa factors cp |
deg |
1150848 |
Modular degree for the optimal curve |
Δ |
-34323907378906054 = -1 · 2 · 7 · 132 · 299 |
Discriminant |
Eigenvalues |
2- -2 3 7+ -3 13+ -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-733054,-241800534] |
[a1,a2,a3,a4,a6] |
Generators |
[9644310:318259943:5832] |
Generators of the group modulo torsion |
j |
-257777464799419276153/203100043662166 |
j-invariant |
L |
7.6795807594238 |
L(r)(E,1)/r! |
Ω |
0.081576495389061 |
Real period |
R |
10.459958435637 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999994444 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68614j1 |
Quadratic twists by: 13 |