Atkin-Lehner |
2+ 3- 5- 11- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
51150be |
Isogeny class |
Conductor |
51150 |
Conductor |
∏ cp |
80 |
Product of Tamagawa factors cp |
deg |
9999360 |
Modular degree for the optimal curve |
Δ |
777254995242000 = 24 · 34 · 53 · 115 · 313 |
Discriminant |
Eigenvalues |
2+ 3- 5- 4 11- 4 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-499778221,4300410337688] |
[a1,a2,a3,a4,a6] |
j |
110444903048508539440990385213/6218039961936 |
j-invariant |
L |
3.8028643309573 |
L(r)(E,1)/r! |
Ω |
0.19014321654065 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
51150bz1 |
Quadratic twists by: 5 |