Atkin-Lehner |
2- 3- 7- 11- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
47124u |
Isogeny class |
Conductor |
47124 |
Conductor |
∏ cp |
56 |
Product of Tamagawa factors cp |
deg |
241920 |
Modular degree for the optimal curve |
Δ |
-7420455971503344 = -1 · 24 · 311 · 77 · 11 · 172 |
Discriminant |
Eigenvalues |
2- 3- 3 7- 11- 1 17+ -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,48759,-58403] |
[a1,a2,a3,a4,a6] |
Generators |
[188:3969:1] |
Generators of the group modulo torsion |
j |
1099108512326912/636184496871 |
j-invariant |
L |
8.2141441445296 |
L(r)(E,1)/r! |
Ω |
0.24907461738015 |
Real period |
R |
0.58890442944766 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999917 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
15708j1 |
Quadratic twists by: -3 |