Atkin-Lehner |
2+ 3- 7- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
81984bc |
Isogeny class |
Conductor |
81984 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
26880 |
Modular degree for the optimal curve |
Δ |
-377782272 = -1 · 215 · 33 · 7 · 61 |
Discriminant |
Eigenvalues |
2+ 3- 0 7- 3 -1 6 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-33,927] |
[a1,a2,a3,a4,a6] |
Generators |
[-9:24:1] |
Generators of the group modulo torsion |
j |
-125000/11529 |
j-invariant |
L |
9.4161797332 |
L(r)(E,1)/r! |
Ω |
1.393112249616 |
Real period |
R |
0.56325801770402 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000351 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81984b1 40992p1 |
Quadratic twists by: -4 8 |