Atkin-Lehner |
3- 5- 7- 13- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
69615w |
Isogeny class |
Conductor |
69615 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
60160 |
Modular degree for the optimal curve |
Δ |
-9591624315 = -1 · 311 · 5 · 72 · 13 · 17 |
Discriminant |
Eigenvalues |
-2 3- 5- 7- 2 13- 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,303,4252] |
[a1,a2,a3,a4,a6] |
Generators |
[40:283:1] |
Generators of the group modulo torsion |
j |
4220112896/13157235 |
j-invariant |
L |
3.979831951453 |
L(r)(E,1)/r! |
Ω |
0.91297864479981 |
Real period |
R |
0.54489663773463 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000114 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23205d1 |
Quadratic twists by: -3 |