Atkin-Lehner |
3- 5+ 17+ 67- |
Signs for the Atkin-Lehner involutions |
Class |
51255c |
Isogeny class |
Conductor |
51255 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
838656 |
Modular degree for the optimal curve |
Δ |
-3081784547647951335 = -1 · 39 · 5 · 178 · 672 |
Discriminant |
Eigenvalues |
1 3- 5+ 0 -4 6 17+ 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-136935,86718496] |
[a1,a2,a3,a4,a6] |
Generators |
[2672217760:-295793609168:33698267] |
Generators of the group modulo torsion |
j |
-389530408392866161/4227413645607615 |
j-invariant |
L |
6.4085826035356 |
L(r)(E,1)/r! |
Ω |
0.21525813603215 |
Real period |
R |
14.885808085237 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000023 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17085b1 |
Quadratic twists by: -3 |