Atkin-Lehner |
2+ 3+ 11+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
9768b |
Isogeny class |
Conductor |
9768 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
4608 |
Modular degree for the optimal curve |
Δ |
-2361492144 = -1 · 24 · 34 · 113 · 372 |
Discriminant |
Eigenvalues |
2+ 3+ 2 -4 11+ 4 4 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,333,0] |
[a1,a2,a3,a4,a6] |
j |
254467069952/147593259 |
j-invariant |
L |
1.7471399638259 |
L(r)(E,1)/r! |
Ω |
0.87356998191297 |
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 |
19536o1 78144bm1 29304s1 107448r1 |
Quadratic twists by: -4 8 -3 -11 |