Atkin-Lehner |
2+ 3+ 7- 13- |
Signs for the Atkin-Lehner involutions |
Class |
13104j |
Isogeny class |
Conductor |
13104 |
Conductor |
∏ cp |
168 |
Product of Tamagawa factors cp |
deg |
80640 |
Modular degree for the optimal curve |
Δ |
-72935267781003264 = -1 · 211 · 39 · 77 · 133 |
Discriminant |
Eigenvalues |
2+ 3+ -1 7- 1 13- 3 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,76437,-10132614] |
[a1,a2,a3,a4,a6] |
Generators |
[1665:-68796:1] |
Generators of the group modulo torsion |
j |
1225217998314/1809323971 |
j-invariant |
L |
4.7245158945281 |
L(r)(E,1)/r! |
Ω |
0.1830113102541 |
Real period |
R |
0.15366328114237 |
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 |
6552n1 52416ee1 13104i1 91728a1 |
Quadratic twists by: -4 8 -3 -7 |