Atkin-Lehner |
2+ 3- 7+ 19- 23- |
Signs for the Atkin-Lehner involutions |
Class |
128478be |
Isogeny class |
Conductor |
128478 |
Conductor |
∏ cp |
720 |
Product of Tamagawa factors cp |
deg |
4331520 |
Modular degree for the optimal curve |
Δ |
-7593354808690947408 = -1 · 24 · 38 · 74 · 195 · 233 |
Discriminant |
Eigenvalues |
2+ 3- -2 7+ -5 0 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-3087222,2091800344] |
[a1,a2,a3,a4,a6] |
Generators |
[-127:-49755:1] [-1438:60369:1] |
Generators of the group modulo torsion |
j |
-1355298417138703689337/3162580095248208 |
j-invariant |
L |
9.0990329292946 |
L(r)(E,1)/r! |
Ω |
0.23507308097604 |
Real period |
R |
0.053760071863016 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000006963 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128478n1 |
Quadratic twists by: -7 |