Atkin-Lehner |
3- 19+ 71+ |
Signs for the Atkin-Lehner involutions |
Class |
12141d |
Isogeny class |
Conductor |
12141 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
7296 |
Modular degree for the optimal curve |
Δ |
-13621364271 = -1 · 312 · 192 · 71 |
Discriminant |
Eigenvalues |
-1 3- -2 -4 -2 0 0 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-1526,23996] |
[a1,a2,a3,a4,a6] |
Generators |
[-42:133:1] [12:79:1] |
Generators of the group modulo torsion |
j |
-538757027353/18684999 |
j-invariant |
L |
3.5077902695626 |
L(r)(E,1)/r! |
Ω |
1.2490394789498 |
Real period |
R |
1.4041951149984 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999991 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4047b1 |
Quadratic twists by: -3 |