Atkin-Lehner |
3+ 11+ 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
9867c |
Isogeny class |
Conductor |
9867 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
Δ |
12698829 = 33 · 112 · 132 · 23 |
Discriminant |
Eigenvalues |
-1 3+ -2 -4 11+ 13+ -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-3309,71886] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:287:1] [8:210:1] |
Generators of the group modulo torsion |
j |
4007026517395537/12698829 |
j-invariant |
L |
2.8403300547216 |
L(r)(E,1)/r! |
Ω |
1.9605654750373 |
Real period |
R |
1.4487300173784 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999974 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
29601f2 108537j2 128271m2 |
Quadratic twists by: -3 -11 13 |