Atkin-Lehner |
2+ 3- 7+ 19- 23- |
Signs for the Atkin-Lehner involutions |
Class |
128478bg |
Isogeny class |
Conductor |
128478 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
311808 |
Modular degree for the optimal curve |
Δ |
-362767397328 = -1 · 24 · 32 · 78 · 19 · 23 |
Discriminant |
Eigenvalues |
2+ 3- -4 7+ 3 -2 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-2623,59042] |
[a1,a2,a3,a4,a6] |
Generators |
[-50:281:1] [-45:316:1] |
Generators of the group modulo torsion |
j |
-346016041/62928 |
j-invariant |
L |
8.8487482376177 |
L(r)(E,1)/r! |
Ω |
0.91830865142586 |
Real period |
R |
0.80299329138046 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999994106 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128478r1 |
Quadratic twists by: -7 |