Atkin-Lehner |
2- 3- 5+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400ef |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
663552 |
Modular degree for the optimal curve |
Δ |
-5169858048000000000 = -1 · 218 · 312 · 59 · 19 |
Discriminant |
Eigenvalues |
2- 3- 5+ 2 0 -2 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-81075,109755250] |
[a1,a2,a3,a4,a6] |
Generators |
[-471:6592:1] |
Generators of the group modulo torsion |
j |
-1263214441/110808000 |
j-invariant |
L |
6.9126363223608 |
L(r)(E,1)/r! |
Ω |
0.19931961458276 |
Real period |
R |
4.3351455500892 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001055 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8550l1 22800cu1 13680bc1 |
Quadratic twists by: -4 -3 5 |