Atkin-Lehner |
2- 3+ 13+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
123708d |
Isogeny class |
Conductor |
123708 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
449280 |
Modular degree for the optimal curve |
Δ |
-6105411396864 = -1 · 28 · 34 · 136 · 61 |
Discriminant |
Eigenvalues |
2- 3+ -1 5 -5 13+ -6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-16956,863784] |
[a1,a2,a3,a4,a6] |
Generators |
[117:684:1] |
Generators of the group modulo torsion |
j |
-436334416/4941 |
j-invariant |
L |
5.3202022923087 |
L(r)(E,1)/r! |
Ω |
0.75837288205265 |
Real period |
R |
3.5076426967434 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000016922 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
732b1 |
Quadratic twists by: 13 |