Atkin-Lehner |
2- 3- 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
121968dm |
Isogeny class |
Conductor |
121968 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
2027520 |
Modular degree for the optimal curve |
Δ |
-8841944716384869936 = -1 · 24 · 314 · 72 · 119 |
Discriminant |
Eigenvalues |
2- 3- -2 7+ 11+ -4 4 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-127776,-144140645] |
[a1,a2,a3,a4,a6] |
Generators |
[28012567:4063257324:1331] |
Generators of the group modulo torsion |
j |
-8388608/321489 |
j-invariant |
L |
5.1340480737937 |
L(r)(E,1)/r! |
Ω |
0.10110487721285 |
Real period |
R |
12.694857910689 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999997518806 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
30492ba1 40656cb1 121968ff1 |
Quadratic twists by: -4 -3 -11 |