Atkin-Lehner |
2- 3+ 7+ 17- |
Signs for the Atkin-Lehner involutions |
Class |
8568h |
Isogeny class |
Conductor |
8568 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
16128 |
Modular degree for the optimal curve |
Δ |
-10707728674608 = -1 · 24 · 39 · 76 · 172 |
Discriminant |
Eigenvalues |
2- 3+ -2 7+ 6 2 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-486,-157491] |
[a1,a2,a3,a4,a6] |
Generators |
[82:595:1] |
Generators of the group modulo torsion |
j |
-40310784/34000561 |
j-invariant |
L |
3.9310683615051 |
L(r)(E,1)/r! |
Ω |
0.32485809227065 |
Real period |
R |
3.0252196690162 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17136b1 68544j1 8568a1 59976ba1 |
Quadratic twists by: -4 8 -3 -7 |