Atkin-Lehner |
2- 3+ 5+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
48960dn |
Isogeny class |
Conductor |
48960 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
32768 |
Modular degree for the optimal curve |
Δ |
-10227548160 = -1 · 218 · 33 · 5 · 172 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -4 -2 -2 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1068,14288] |
[a1,a2,a3,a4,a6] |
Generators |
[-4:136:1] [13:51:1] |
Generators of the group modulo torsion |
j |
-19034163/1445 |
j-invariant |
L |
8.03414698541 |
L(r)(E,1)/r! |
Ω |
1.2624883436843 |
Real period |
R |
1.5909348837956 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999987 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
48960g1 12240bj1 48960dz1 |
Quadratic twists by: -4 8 -3 |