Atkin-Lehner |
2+ 3- 11- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
40128x |
Isogeny class |
Conductor |
40128 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
147456 |
Modular degree for the optimal curve |
Δ |
7195211071488 = 226 · 33 · 11 · 192 |
Discriminant |
Eigenvalues |
2+ 3- 2 0 11- 2 2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-143297,20830623] |
[a1,a2,a3,a4,a6] |
Generators |
[-293:6144:1] |
Generators of the group modulo torsion |
j |
1241361053832817/27447552 |
j-invariant |
L |
8.6635823413887 |
L(r)(E,1)/r! |
Ω |
0.68840433184194 |
Real period |
R |
2.0975033471507 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999997 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
40128bi1 1254g1 120384s1 |
Quadratic twists by: -4 8 -3 |