Atkin-Lehner |
2- 3+ 13- 23- |
Signs for the Atkin-Lehner involutions |
Class |
86112u |
Isogeny class |
Conductor |
86112 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
28672 |
Modular degree for the optimal curve |
Δ |
1135128384 = 26 · 33 · 134 · 23 |
Discriminant |
Eigenvalues |
2- 3+ -2 -2 -4 13- 2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-261,-80] |
[a1,a2,a3,a4,a6] |
Generators |
[23:78:1] [32:156:1] |
Generators of the group modulo torsion |
j |
1137893184/656903 |
j-invariant |
L |
9.1129927306084 |
L(r)(E,1)/r! |
Ω |
1.2964339856069 |
Real period |
R |
1.757319082941 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998764 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
86112s1 86112a1 |
Quadratic twists by: -4 -3 |