Atkin-Lehner |
2+ 3- 13- 53+ |
Signs for the Atkin-Lehner involutions |
Class |
4134d |
Isogeny class |
Conductor |
4134 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
-5804136 = -1 · 23 · 34 · 132 · 53 |
Discriminant |
Eigenvalues |
2+ 3- 1 -2 1 13- -1 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-98,380] |
[a1,a2,a3,a4,a6] |
Generators |
[0:19:1] |
Generators of the group modulo torsion |
j |
-102568953241/5804136 |
j-invariant |
L |
3.3030819819113 |
L(r)(E,1)/r! |
Ω |
2.3667331074277 |
Real period |
R |
0.17445365784723 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
33072p1 12402l1 103350bf1 53742s1 |
Quadratic twists by: -4 -3 5 13 |