Atkin-Lehner |
3- 19+ 79+ |
Signs for the Atkin-Lehner involutions |
Class |
13509b |
Isogeny class |
Conductor |
13509 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
239616 |
Modular degree for the optimal curve |
Δ |
-141979036507509339 = -1 · 312 · 193 · 794 |
Discriminant |
Eigenvalues |
-2 3- 3 -1 -1 6 -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-300801,66036208] |
[a1,a2,a3,a4,a6] |
j |
-4128896637887131648/194758623467091 |
j-invariant |
L |
1.2937053803908 |
L(r)(E,1)/r! |
Ω |
0.32342634509769 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
4503b1 |
Quadratic twists by: -3 |