Atkin-Lehner |
3+ 7+ 13- 23- |
Signs for the Atkin-Lehner involutions |
Class |
81627j |
Isogeny class |
Conductor |
81627 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
419328 |
Modular degree for the optimal curve |
Δ |
15811531259629833 = 33 · 74 · 139 · 23 |
Discriminant |
Eigenvalues |
-1 3+ 0 7+ -2 13- -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-64308,1646172] |
[a1,a2,a3,a4,a6] |
Generators |
[20012:2820828:1] |
Generators of the group modulo torsion |
j |
2773505125/1491021 |
j-invariant |
L |
2.0784996638714 |
L(r)(E,1)/r! |
Ω |
0.34288151316827 |
Real period |
R |
6.0618598024115 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000010616 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
81627o1 |
Quadratic twists by: 13 |