Atkin-Lehner |
2- 3+ 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
120384ce |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-4272156573696 = -1 · 221 · 33 · 11 · 193 |
Discriminant |
Eigenvalues |
2- 3+ -3 4 11+ 4 -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,2196,91216] |
[a1,a2,a3,a4,a6] |
Generators |
[-16:228:1] |
Generators of the group modulo torsion |
j |
165469149/603592 |
j-invariant |
L |
6.9393616355299 |
L(r)(E,1)/r! |
Ω |
0.55284368025612 |
Real period |
R |
1.0460102256914 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999998882438 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120384g1 30096p1 120384cl2 |
Quadratic twists by: -4 8 -3 |