Atkin-Lehner |
3- 13+ 19+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
51129f |
Isogeny class |
Conductor |
51129 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
112128 |
Modular degree for the optimal curve |
Δ |
-209271559419 = -1 · 36 · 134 · 19 · 232 |
Discriminant |
Eigenvalues |
-2 3- -1 -3 3 13+ 1 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-15573,748332] |
[a1,a2,a3,a4,a6] |
Generators |
[-142:310:1] [11:760:1] |
Generators of the group modulo torsion |
j |
-572945133039616/287066611 |
j-invariant |
L |
4.6524332035035 |
L(r)(E,1)/r! |
Ω |
0.98671094119502 |
Real period |
R |
0.58938654286502 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999986 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
5681b1 |
Quadratic twists by: -3 |