Atkin-Lehner |
2- 3+ 5- 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
29370z |
Isogeny class |
Conductor |
29370 |
Conductor |
∏ cp |
15 |
Product of Tamagawa factors cp |
deg |
33600 |
Modular degree for the optimal curve |
Δ |
-11748000 = -1 · 25 · 3 · 53 · 11 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 5- -1 11- 2 -6 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-10285,397187] |
[a1,a2,a3,a4,a6] |
Generators |
[57:-14:1] |
Generators of the group modulo torsion |
j |
-120320392325340241/11748000 |
j-invariant |
L |
7.5710959059852 |
L(r)(E,1)/r! |
Ω |
1.7391395835857 |
Real period |
R |
0.29022381632244 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
88110i1 |
Quadratic twists by: -3 |