Atkin-Lehner |
2+ 3- 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
86112k |
Isogeny class |
Conductor |
86112 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
1720320 |
Modular degree for the optimal curve |
Δ |
-957363722708372928 = -1 · 26 · 316 · 134 · 233 |
Discriminant |
Eigenvalues |
2+ 3- -4 2 0 13+ 8 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,22803,47057020] |
[a1,a2,a3,a4,a6] |
Generators |
[1688:69966:1] |
Generators of the group modulo torsion |
j |
28105555379264/20519627115663 |
j-invariant |
L |
4.7309578539521 |
L(r)(E,1)/r! |
Ω |
0.21740643638777 |
Real period |
R |
1.8134076185791 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999938017 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
86112ba1 28704r1 |
Quadratic twists by: -4 -3 |