Atkin-Lehner |
3+ 13- 17- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
45747b |
Isogeny class |
Conductor |
45747 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
3328 |
Modular degree for the optimal curve |
Δ |
-137241 = -1 · 33 · 13 · 17 · 23 |
Discriminant |
Eigenvalues |
-1 3+ 1 3 2 13- 17- 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-2,18] |
[a1,a2,a3,a4,a6] |
Generators |
[2:3:1] |
Generators of the group modulo torsion |
j |
-19683/5083 |
j-invariant |
L |
5.0014334285945 |
L(r)(E,1)/r! |
Ω |
2.6686086014441 |
Real period |
R |
0.93708635764341 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999766 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
45747a1 |
Quadratic twists by: -3 |