Atkin-Lehner |
2+ 3+ 11- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
27456p |
Isogeny class |
Conductor |
27456 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
32768 |
Modular degree for the optimal curve |
Δ |
-245949530112 = -1 · 218 · 38 · 11 · 13 |
Discriminant |
Eigenvalues |
2+ 3+ 2 0 11- 13+ -6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1537,33793] |
[a1,a2,a3,a4,a6] |
j |
-1532808577/938223 |
j-invariant |
L |
1.8272601659042 |
L(r)(E,1)/r! |
Ω |
0.91363008295209 |
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 |
27456bz1 429b1 82368w1 |
Quadratic twists by: -4 8 -3 |