Atkin-Lehner |
3+ 5- 47- |
Signs for the Atkin-Lehner involutions |
Class |
33135f |
Isogeny class |
Conductor |
33135 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
1299456 |
Modular degree for the optimal curve |
Δ |
2169803497052971125 = 36 · 53 · 478 |
Discriminant |
Eigenvalues |
-1 3+ 5- 4 3 0 0 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-13598650,19295737010] |
[a1,a2,a3,a4,a6] |
Generators |
[2123:-792:1] |
Generators of the group modulo torsion |
j |
11679607249441/91125 |
j-invariant |
L |
3.9040644724568 |
L(r)(E,1)/r! |
Ω |
0.23359525834378 |
Real period |
R |
2.7854906674456 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999995 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
99405h1 33135b1 |
Quadratic twists by: -3 -47 |