Atkin-Lehner |
11- 71- |
Signs for the Atkin-Lehner involutions |
Class |
8591b |
Isogeny class |
Conductor |
8591 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
12960 |
Modular degree for the optimal curve |
Δ |
167414286061 = 119 · 71 |
Discriminant |
Eigenvalues |
0 0 -1 -3 11- -1 3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-97768,-11766373] |
[a1,a2,a3,a4,a6] |
Generators |
[451:5989:1] |
Generators of the group modulo torsion |
j |
58338840674304/94501 |
j-invariant |
L |
2.4318918902242 |
L(r)(E,1)/r! |
Ω |
0.26999170043248 |
Real period |
R |
2.2518209692453 |
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 |
77319p1 781b1 |
Quadratic twists by: -3 -11 |