Atkin-Lehner |
3+ 5+ 13- 59+ |
Signs for the Atkin-Lehner involutions |
Class |
57525a |
Isogeny class |
Conductor |
57525 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
-10082492138671875 = -1 · 33 · 511 · 133 · 592 |
Discriminant |
Eigenvalues |
0 3+ 5+ -3 1 13- -3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-327633,72452918] |
[a1,a2,a3,a4,a6] |
Generators |
[-172:11121:1] [452:4062:1] |
Generators of the group modulo torsion |
j |
-248924662605807616/645279496875 |
j-invariant |
L |
6.6335608537864 |
L(r)(E,1)/r! |
Ω |
0.40851850752321 |
Real period |
R |
0.67658714064999 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
11505e1 |
Quadratic twists by: 5 |