Atkin-Lehner |
2- 3+ 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
120384bz |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
76800 |
Modular degree for the optimal curve |
Δ |
-134799261696 = -1 · 215 · 39 · 11 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 1 0 11+ 0 -5 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-972,21168] |
[a1,a2,a3,a4,a6] |
Generators |
[-2:152:1] [24:108:1] |
Generators of the group modulo torsion |
j |
-157464/209 |
j-invariant |
L |
12.8580430251 |
L(r)(E,1)/r! |
Ω |
0.93624732184486 |
Real period |
R |
1.7166995739267 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999977378 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120384cj1 60192b1 120384cg1 |
Quadratic twists by: -4 8 -3 |