Atkin-Lehner |
7- 29+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
86681d |
Isogeny class |
Conductor |
86681 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
645120 |
Modular degree for the optimal curve |
Δ |
-330676717605227 = -1 · 77 · 29 · 614 |
Discriminant |
Eigenvalues |
-2 -3 0 7- 2 -4 -6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-27685,-1977138] |
[a1,a2,a3,a4,a6] |
Generators |
[217:1494:1] |
Generators of the group modulo torsion |
j |
-19946608128000/2810705723 |
j-invariant |
L |
1.0648146972869 |
L(r)(E,1)/r! |
Ω |
0.1836226108924 |
Real period |
R |
0.72486626605581 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.00000000631 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
12383c1 |
Quadratic twists by: -7 |