Atkin-Lehner |
2+ 3+ 13+ 41+ |
Signs for the Atkin-Lehner involutions |
Class |
51168b |
Isogeny class |
Conductor |
51168 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
13056 |
Modular degree for the optimal curve |
Δ |
-4195776 = -1 · 26 · 3 · 13 · 412 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -2 -4 13+ -8 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-14,-96] |
[a1,a2,a3,a4,a6] |
Generators |
[7:10:1] |
Generators of the group modulo torsion |
j |
-5088448/65559 |
j-invariant |
L |
2.4255286540481 |
L(r)(E,1)/r! |
Ω |
1.0521349974413 |
Real period |
R |
2.3053397709677 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000082 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51168g1 102336cn1 |
Quadratic twists by: -4 8 |