Atkin-Lehner |
2- 3- 11- 43- |
Signs for the Atkin-Lehner involutions |
Class |
8514k |
Isogeny class |
Conductor |
8514 |
Conductor |
∏ cp |
168 |
Product of Tamagawa factors cp |
deg |
169344 |
Modular degree for the optimal curve |
Δ |
-205606486627762176 = -1 · 214 · 315 · 11 · 433 |
Discriminant |
Eigenvalues |
2- 3- -3 -1 11- -4 3 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1756364,-895747633] |
[a1,a2,a3,a4,a6] |
Generators |
[2781:123997:1] |
Generators of the group modulo torsion |
j |
-821938895581650775417/282039076306944 |
j-invariant |
L |
5.0866217450586 |
L(r)(E,1)/r! |
Ω |
0.065570275313848 |
Real period |
R |
0.46175664571076 |
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 |
68112bp1 2838b1 93654q1 |
Quadratic twists by: -4 -3 -11 |