Atkin-Lehner |
2+ 3+ 5+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
127680d |
Isogeny class |
Conductor |
127680 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
229376 |
Modular degree for the optimal curve |
Δ |
30643200 = 210 · 32 · 52 · 7 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ 7+ -4 -2 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-39901,-3054515] |
[a1,a2,a3,a4,a6] |
Generators |
[669:16408:1] |
Generators of the group modulo torsion |
j |
6860977263302656/29925 |
j-invariant |
L |
4.0341150160014 |
L(r)(E,1)/r! |
Ω |
0.33779460007832 |
Real period |
R |
5.9712544665812 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999677552 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
127680fo1 15960i1 |
Quadratic twists by: -4 8 |