Atkin-Lehner |
2- 3+ 23- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
51336m |
Isogeny class |
Conductor |
51336 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
20736 |
Modular degree for the optimal curve |
Δ |
-3592698624 = -1 · 28 · 39 · 23 · 31 |
Discriminant |
Eigenvalues |
2- 3+ -1 -2 -4 0 -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-108,2916] |
[a1,a2,a3,a4,a6] |
Generators |
[0:54:1] |
Generators of the group modulo torsion |
j |
-27648/713 |
j-invariant |
L |
3.6597160552131 |
L(r)(E,1)/r! |
Ω |
1.175460694925 |
Real period |
R |
0.77835781133022 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999645 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
102672b1 51336a1 |
Quadratic twists by: -4 -3 |