Atkin-Lehner |
2+ 3- 17- 29- |
Signs for the Atkin-Lehner involutions |
Class |
47328p |
Isogeny class |
Conductor |
47328 |
Conductor |
∏ cp |
12 |
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] |
j |
-5747651544305152/386019 |
j-invariant |
L |
7.3299369512089 |
L(r)(E,1)/r! |
Ω |
0.15270701982761 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
4 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47328t1 94656m1 |
Quadratic twists by: -4 8 |