Atkin-Lehner |
2+ 3- 5+ 7+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
127680cl |
Isogeny class |
Conductor |
127680 |
Conductor |
∏ cp |
176 |
Product of Tamagawa factors cp |
deg |
9461760 |
Modular degree for the optimal curve |
Δ |
4323379956940800 = 220 · 311 · 52 · 72 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 5+ 7+ -6 -2 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-112192801,457362014015] |
[a1,a2,a3,a4,a6] |
Generators |
[6122:-945:1] |
Generators of the group modulo torsion |
j |
595770186172725915913801/16492385700 |
j-invariant |
L |
5.2251242657835 |
L(r)(E,1)/r! |
Ω |
0.23047997543505 |
Real period |
R |
0.51524138448611 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.00000002175 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
127680dy1 3990h1 |
Quadratic twists by: -4 8 |