Atkin-Lehner |
2+ 3+ 19+ 73- |
Signs for the Atkin-Lehner involutions |
Class |
99864a |
Isogeny class |
Conductor |
99864 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
14336 |
Modular degree for the optimal curve |
Δ |
-11384496 = -1 · 24 · 33 · 192 · 73 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -4 0 -4 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,54,-55] |
[a1,a2,a3,a4,a6] |
Generators |
[4:15:1] [17:76:1] |
Generators of the group modulo torsion |
j |
40310784/26353 |
j-invariant |
L |
8.5342162063757 |
L(r)(E,1)/r! |
Ω |
1.2941586536272 |
Real period |
R |
3.2972063289389 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999995253 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
99864h1 |
Quadratic twists by: -3 |