Atkin-Lehner |
3- 13- 23+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
83421o |
Isogeny class |
Conductor |
83421 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
5971968 |
Modular degree for the optimal curve |
Δ |
-1.8211244597898E+22 |
Discriminant |
Eigenvalues |
-1 3- -2 2 -4 13- 4 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-14919251,-23107395630] |
[a1,a2,a3,a4,a6] |
Generators |
[643330:-24174279:125] |
Generators of the group modulo torsion |
j |
-503775703473363124555753/24981131135662997607 |
j-invariant |
L |
3.3791471033733 |
L(r)(E,1)/r! |
Ω |
0.038298292339924 |
Real period |
R |
11.029039725293 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000006954 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
27807i1 |
Quadratic twists by: -3 |