Atkin-Lehner |
2+ 3+ 83- |
Signs for the Atkin-Lehner involutions |
Class |
7968a |
Isogeny class |
Conductor |
7968 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
768 |
Modular degree for the optimal curve |
Δ |
-1019904 = -1 · 212 · 3 · 83 |
Discriminant |
Eigenvalues |
2+ 3+ -1 -2 -5 -4 -4 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1,49] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:4:1] [0:7:1] |
Generators of the group modulo torsion |
j |
-64/249 |
j-invariant |
L |
4.4482592204313 |
L(r)(E,1)/r! |
Ω |
2.2246935056926 |
Real period |
R |
0.49987326445748 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.9999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7968f1 15936i1 23904q1 |
Quadratic twists by: -4 8 -3 |