Atkin-Lehner |
2+ 3- 13- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
86112l |
Isogeny class |
Conductor |
86112 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
833280 |
Modular degree for the optimal curve |
Δ |
-132167805997953024 = -1 · 212 · 36 · 13 · 237 |
Discriminant |
Eigenvalues |
2+ 3- -1 4 -5 13- -4 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-148008,28040816] |
[a1,a2,a3,a4,a6] |
Generators |
[1277980:36960644:1331] |
Generators of the group modulo torsion |
j |
-120085841645056/44262730811 |
j-invariant |
L |
6.6289573877334 |
L(r)(E,1)/r! |
Ω |
0.3093229265358 |
Real period |
R |
10.715270061631 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999341 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
86112bn1 9568l1 |
Quadratic twists by: -4 -3 |