Atkin-Lehner |
2+ 3+ 13+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
47658b |
Isogeny class |
Conductor |
47658 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
709632 |
Modular degree for the optimal curve |
Δ |
-353168387080620228 = -1 · 22 · 311 · 139 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ -2 1 3 13+ -6 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,139084,20525796] |
[a1,a2,a3,a4,a6] |
Generators |
[-125:1161:1] |
Generators of the group modulo torsion |
j |
61643918316527/73168088292 |
j-invariant |
L |
2.5783326650036 |
L(r)(E,1)/r! |
Ω |
0.20236587066486 |
Real period |
R |
1.5926182713851 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999951 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3666k1 |
Quadratic twists by: 13 |