Atkin-Lehner |
3- 5- 11- 67- |
Signs for the Atkin-Lehner involutions |
Class |
33165r |
Isogeny class |
Conductor |
33165 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
768000 |
Modular degree for the optimal curve |
Δ |
-4089816728391796875 = -1 · 36 · 58 · 118 · 67 |
Discriminant |
Eigenvalues |
-2 3- 5- -2 11- -6 -3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,175533,-93090870] |
[a1,a2,a3,a4,a6] |
Generators |
[938:-29948:1] |
Generators of the group modulo torsion |
j |
820488521674059776/5610173838671875 |
j-invariant |
L |
2.1852415337571 |
L(r)(E,1)/r! |
Ω |
0.12308839916327 |
Real period |
R |
0.13869868808541 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3685a1 |
Quadratic twists by: -3 |