Atkin-Lehner |
3- 5+ 7+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
21945w |
Isogeny class |
Conductor |
21945 |
Conductor |
∏ cp |
660 |
Product of Tamagawa factors cp |
deg |
475200 |
Modular degree for the optimal curve |
Δ |
-239714397645705675 = -1 · 311 · 52 · 72 · 115 · 193 |
Discriminant |
Eigenvalues |
-2 3- 5+ 7+ 11- -5 -5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,63674,22751146] |
[a1,a2,a3,a4,a6] |
Generators |
[-143:3277:1] [-1150637930729968253003208991:-81691859061094501403859893711:18911475197260804320245299] |
Generators of the group modulo torsion |
j |
28549814500156461056/239714397645705675 |
j-invariant |
L |
4.5246838188967 |
L(r)(E,1)/r! |
Ω |
0.22871830058572 |
Real period |
R |
0.029973909067292 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
65835bd1 109725z1 |
Quadratic twists by: -3 5 |