Atkin-Lehner |
2+ 3- 11- |
Signs for the Atkin-Lehner involutions |
Class |
69696ck |
Isogeny class |
Conductor |
69696 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
Δ |
4.5732703447359E+21 |
Discriminant |
Eigenvalues |
2+ 3- 2 4 11- -2 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-85387764,-303680321120] |
[a1,a2,a3,a4,a6] |
Generators |
[-76556824141911448333941346272979550:-44372386145551397228141439488231952:14410059650005610440965814578125] |
Generators of the group modulo torsion |
j |
13015685560572352/864536409 |
j-invariant |
L |
8.9564521138483 |
L(r)(E,1)/r! |
Ω |
0.049665221339165 |
Real period |
R |
45.084124627958 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999996965 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
69696cn2 34848cf1 23232cf2 6336bb2 |
Quadratic twists by: -4 8 -3 -11 |