Atkin-Lehner |
2- 3+ 5+ 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
127680du |
Isogeny class |
Conductor |
127680 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
1769472 |
Modular degree for the optimal curve |
Δ |
-1096762848706560000 = -1 · 242 · 3 · 54 · 7 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 7- -4 2 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,245119,18811425] |
[a1,a2,a3,a4,a6] |
Generators |
[15027856:-918559477:4096] |
Generators of the group modulo torsion |
j |
6213165856218719/4183818240000 |
j-invariant |
L |
4.7908064293165 |
L(r)(E,1)/r! |
Ω |
0.17332174021408 |
Real period |
R |
13.820558242818 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000038753 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
127680cf1 31920cc1 |
Quadratic twists by: -4 8 |