Atkin-Lehner |
2+ 3- 5- 11+ 13+ |
Signs for the Atkin-Lehner involutions |
Class |
51480p |
Isogeny class |
Conductor |
51480 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-133436160 = -1 · 28 · 36 · 5 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 5- -2 11+ 13+ -3 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-12,-556] |
[a1,a2,a3,a4,a6] |
Generators |
[10:18:1] |
Generators of the group modulo torsion |
j |
-1024/715 |
j-invariant |
L |
5.33309592977 |
L(r)(E,1)/r! |
Ω |
0.83158025092749 |
Real period |
R |
0.80165082140541 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000011 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
102960bo1 5720f1 |
Quadratic twists by: -4 -3 |