Atkin-Lehner |
2+ 3+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
51264f |
Isogeny class |
Conductor |
51264 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
11520 |
Modular degree for the optimal curve |
Δ |
-112114368 = -1 · 26 · 39 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -2 -4 2 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,54,-486] |
[a1,a2,a3,a4,a6] |
Generators |
[9:27:1] [241:3743:1] |
Generators of the group modulo torsion |
j |
13824/89 |
j-invariant |
L |
8.1948516957422 |
L(r)(E,1)/r! |
Ω |
0.93569096059248 |
Real period |
R |
4.3790375459818 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51264e1 25632b1 51264c1 |
Quadratic twists by: -4 8 -3 |