Atkin-Lehner |
2+ 3- 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
60192c |
Isogeny class |
Conductor |
60192 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
77824 |
Modular degree for the optimal curve |
Δ |
321786432 = 26 · 37 · 112 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 0 -4 11+ 4 -6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-20685,1145068] |
[a1,a2,a3,a4,a6] |
Generators |
[-79:1512:1] [8:990:1] |
Generators of the group modulo torsion |
j |
20978903512000/6897 |
j-invariant |
L |
9.2423590178449 |
L(r)(E,1)/r! |
Ω |
1.3834799222192 |
Real period |
R |
1.6701288666018 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999956 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
60192y1 120384bq1 20064s1 |
Quadratic twists by: -4 8 -3 |