Atkin-Lehner |
2+ 3+ 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
120384i |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
165888 |
Modular degree for the optimal curve |
Δ |
-8155355332608 = -1 · 214 · 39 · 113 · 19 |
Discriminant |
Eigenvalues |
2+ 3+ -2 0 11- 1 -1 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-9936,-405216] |
[a1,a2,a3,a4,a6] |
Generators |
[969:29997:1] |
Generators of the group modulo torsion |
j |
-336393216/25289 |
j-invariant |
L |
5.2679764850443 |
L(r)(E,1)/r! |
Ω |
0.23806458726647 |
Real period |
R |
3.6880582885732 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000007468 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120384ca1 15048a1 120384d1 |
Quadratic twists by: -4 8 -3 |