Atkin-Lehner |
2- 3+ 7- 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
52668j |
Isogeny class |
Conductor |
52668 |
Conductor |
∏ cp |
144 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
-2220059218608 = -1 · 24 · 33 · 76 · 112 · 192 |
Discriminant |
Eigenvalues |
2- 3+ -2 7- 11+ -2 -6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-6396,209529] |
[a1,a2,a3,a4,a6] |
Generators |
[5220:-30723:64] [40:-133:1] |
Generators of the group modulo torsion |
j |
-66983113506816/5139025969 |
j-invariant |
L |
8.907392273327 |
L(r)(E,1)/r! |
Ω |
0.80615457695777 |
Real period |
R |
0.30692322566931 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
52668l1 |
Quadratic twists by: -3 |