Atkin-Lehner |
3- 5- 7- 23- |
Signs for the Atkin-Lehner involutions |
Class |
12075x |
Isogeny class |
Conductor |
12075 |
Conductor |
∏ cp |
405 |
Product of Tamagawa factors cp |
deg |
129600 |
Modular degree for the optimal curve |
Δ |
-1572262424307421875 = -1 · 39 · 58 · 75 · 233 |
Discriminant |
Eigenvalues |
0 3- 5- 7- -3 2 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-77833,60878494] |
[a1,a2,a3,a4,a6] |
Generators |
[-406:5071:1] |
Generators of the group modulo torsion |
j |
-133493637775360/4024991806227 |
j-invariant |
L |
4.5785085102349 |
L(r)(E,1)/r! |
Ω |
0.22335614183472 |
Real period |
R |
0.45552646426023 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
36225cf1 12075a1 84525bf1 |
Quadratic twists by: -3 5 -7 |