Atkin-Lehner |
2+ 3- 7- 19- |
Signs for the Atkin-Lehner involutions |
Class |
12768k |
Isogeny class |
Conductor |
12768 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
-11034539712 = -1 · 26 · 33 · 72 · 194 |
Discriminant |
Eigenvalues |
2+ 3- 4 7- 2 6 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-806,-10428] |
[a1,a2,a3,a4,a6] |
j |
-905915267776/172414683 |
j-invariant |
L |
5.3207266157447 |
L(r)(E,1)/r! |
Ω |
0.4433938846454 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
12768l1 25536q2 38304br1 89376j1 |
Quadratic twists by: -4 8 -3 -7 |