Atkin-Lehner |
2- 7+ 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68614u |
Isogeny class |
Conductor |
68614 |
Conductor |
∏ cp |
42 |
Product of Tamagawa factors cp |
deg |
1546272 |
Modular degree for the optimal curve |
Δ |
-4514567155024396288 = -1 · 221 · 7 · 139 · 29 |
Discriminant |
Eigenvalues |
2- -2 0 7+ -2 13- -7 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-207113,-108491111] |
[a1,a2,a3,a4,a6] |
Generators |
[690:8443:1] |
Generators of the group modulo torsion |
j |
-92652203125/425721856 |
j-invariant |
L |
5.611252039383 |
L(r)(E,1)/r! |
Ω |
0.10143732706255 |
Real period |
R |
1.3170816198516 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999993987 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68614l1 |
Quadratic twists by: 13 |