Atkin-Lehner |
2+ 3+ 7+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
9744a |
Isogeny class |
Conductor |
9744 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
Δ |
273768671232 = 211 · 33 · 7 · 294 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7+ -4 -2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-8344,-289520] |
[a1,a2,a3,a4,a6] |
Generators |
[-54:26:1] |
Generators of the group modulo torsion |
j |
31373913421874/133676109 |
j-invariant |
L |
2.6691307406937 |
L(r)(E,1)/r! |
Ω |
0.49964663759886 |
Real period |
R |
2.6710184156554 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4872g4 38976br3 29232h3 68208t3 |
Quadratic twists by: -4 8 -3 -7 |