Atkin-Lehner |
2+ 3- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
65472u |
Isogeny class |
Conductor |
65472 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
1437696 |
Modular degree for the optimal curve |
Δ |
-581352644891639808 = -1 · 231 · 38 · 113 · 31 |
Discriminant |
Eigenvalues |
2+ 3- -2 -1 11+ 0 -5 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3776609,2823867135] |
[a1,a2,a3,a4,a6] |
Generators |
[787:18432:1] |
Generators of the group modulo torsion |
j |
-22724271869580547993/2217684344832 |
j-invariant |
L |
5.8342839504008 |
L(r)(E,1)/r! |
Ω |
0.27823634150602 |
Real period |
R |
0.65527519681464 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000476 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
65472bu1 2046c1 |
Quadratic twists by: -4 8 |