Atkin-Lehner |
2+ 3- 23- |
Signs for the Atkin-Lehner involutions |
Class |
50784k |
Isogeny class |
Conductor |
50784 |
Conductor |
∏ cp |
48 |
Product of Tamagawa factors cp |
deg |
494592 |
Modular degree for the optimal curve |
Δ |
-25981705452589056 = -1 · 212 · 34 · 238 |
Discriminant |
Eigenvalues |
2+ 3- 1 2 -4 -3 6 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-762465,-256629969] |
[a1,a2,a3,a4,a6] |
Generators |
[3879:234876:1] |
Generators of the group modulo torsion |
j |
-152827456/81 |
j-invariant |
L |
8.4061530176787 |
L(r)(E,1)/r! |
Ω |
0.080779419366505 |
Real period |
R |
2.1679802756827 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000035 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
50784s1 101568g1 50784l1 |
Quadratic twists by: -4 8 -23 |