Atkin-Lehner |
2+ 3- 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312bo |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
829440 |
Modular degree for the optimal curve |
Δ |
404910339520462848 = 224 · 33 · 197 |
Discriminant |
Eigenvalues |
2+ 3- 0 -4 0 -4 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-185313,-2407041] |
[a1,a2,a3,a4,a6] |
Generators |
[-355:4332:1] |
Generators of the group modulo torsion |
j |
57066625/32832 |
j-invariant |
L |
5.9169397598179 |
L(r)(E,1)/r! |
Ω |
0.25030337737634 |
Real period |
R |
1.9699227334041 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999995269 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69312cm1 2166b1 3648b1 |
Quadratic twists by: -4 8 -19 |