Atkin-Lehner |
2- 3- 11- 61- |
Signs for the Atkin-Lehner involutions |
Class |
32208r |
Isogeny class |
Conductor |
32208 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
16128 |
Modular degree for the optimal curve |
Δ |
-9498525696 = -1 · 219 · 33 · 11 · 61 |
Discriminant |
Eigenvalues |
2- 3- 1 2 11- -1 0 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-1320,18612] |
[a1,a2,a3,a4,a6] |
Generators |
[-18:192:1] |
Generators of the group modulo torsion |
j |
-62146192681/2318976 |
j-invariant |
L |
8.2419267398127 |
L(r)(E,1)/r! |
Ω |
1.2858413226421 |
Real period |
R |
0.53414617824416 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4026a1 128832y1 96624bl1 |
Quadratic twists by: -4 8 -3 |