Atkin-Lehner |
2+ 3+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
8256i |
Isogeny class |
Conductor |
8256 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
-13866909696 = -1 · 214 · 39 · 43 |
Discriminant |
Eigenvalues |
2+ 3+ -3 5 3 1 -6 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-177,-5679] |
[a1,a2,a3,a4,a6] |
Generators |
[47:296:1] |
Generators of the group modulo torsion |
j |
-37642192/846369 |
j-invariant |
L |
3.6730704254097 |
L(r)(E,1)/r! |
Ω |
0.54226332785955 |
Real period |
R |
3.3867958948176 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8256bt1 516d1 24768s1 |
Quadratic twists by: -4 8 -3 |