Atkin-Lehner |
2+ 3- 13+ 47- |
Signs for the Atkin-Lehner involutions |
Class |
47658j |
Isogeny class |
Conductor |
47658 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
137088 |
Modular degree for the optimal curve |
Δ |
-17199619503768 = -1 · 23 · 36 · 137 · 47 |
Discriminant |
Eigenvalues |
2+ 3- 0 -2 -6 13+ 3 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-9806,422840] |
[a1,a2,a3,a4,a6] |
Generators |
[66:220:1] |
Generators of the group modulo torsion |
j |
-21601086625/3563352 |
j-invariant |
L |
4.1978692120144 |
L(r)(E,1)/r! |
Ω |
0.66754110561145 |
Real period |
R |
0.26202314089152 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000043 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3666n1 |
Quadratic twists by: 13 |