Atkin-Lehner |
2- 3+ 7+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
12768l |
Isogeny class |
Conductor |
12768 |
Conductor |
∏ cp |
8 |
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 |
2.4540310630025 |
L(r)(E,1)/r! |
Ω |
1.2270155315013 |
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 |
12768k1 25536bk2 38304m1 89376cz1 |
Quadratic twists by: -4 8 -3 -7 |