Atkin-Lehner |
2- 17+ 79- |
Signs for the Atkin-Lehner involutions |
Class |
2686c |
Isogeny class |
Conductor |
2686 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
25344 |
Modular degree for the optimal curve |
Δ |
168669635866624 = 212 · 174 · 793 |
Discriminant |
Eigenvalues |
2- 1 -3 5 -6 -1 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-89132,10215824] |
[a1,a2,a3,a4,a6] |
Generators |
[158:210:1] |
Generators of the group modulo torsion |
j |
78311397007706818753/168669635866624 |
j-invariant |
L |
4.8876701459678 |
L(r)(E,1)/r! |
Ω |
0.57380812790478 |
Real period |
R |
1.0647440120391 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
21488e1 85952f1 24174g1 67150f1 |
Quadratic twists by: -4 8 -3 5 |