Atkin-Lehner |
2- 3+ 17- 29- |
Signs for the Atkin-Lehner involutions |
Class |
47328t |
Isogeny class |
Conductor |
47328 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
159744 |
Modular degree for the optimal curve |
Δ |
-1581133824 = -1 · 212 · 33 · 17 · 292 |
Discriminant |
Eigenvalues |
2- 3+ 3 -4 -5 -1 17- -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-59709,5635701] |
[a1,a2,a3,a4,a6] |
Generators |
[-5:2436:1] [140:29:1] |
Generators of the group modulo torsion |
j |
-5747651544305152/386019 |
j-invariant |
L |
8.5154117446692 |
L(r)(E,1)/r! |
Ω |
1.1385938007235 |
Real period |
R |
1.869721172568 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999994 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47328p1 94656ba1 |
Quadratic twists by: -4 8 |