Atkin-Lehner |
2+ 3+ 5- 11+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
47850u |
Isogeny class |
Conductor |
47850 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
241920 |
Modular degree for the optimal curve |
Δ |
-1151127450000000 = -1 · 27 · 38 · 58 · 112 · 29 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -2 11+ 0 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,17050,1396500] |
[a1,a2,a3,a4,a6] |
Generators |
[-65:170:1] [-170:8185:8] |
Generators of the group modulo torsion |
j |
1403127146615/2946886272 |
j-invariant |
L |
5.8049258778188 |
L(r)(E,1)/r! |
Ω |
0.338034267075 |
Real period |
R |
1.4310496605489 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47850cl1 |
Quadratic twists by: 5 |