Atkin-Lehner |
2- 3- 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
60192z |
Isogeny class |
Conductor |
60192 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
51840 |
Modular degree for the optimal curve |
Δ |
-309773071872 = -1 · 29 · 36 · 112 · 193 |
Discriminant |
Eigenvalues |
2- 3- 2 -1 11- -5 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-939,-28978] |
[a1,a2,a3,a4,a6] |
Generators |
[41:38:1] |
Generators of the group modulo torsion |
j |
-245314376/829939 |
j-invariant |
L |
7.1302284805722 |
L(r)(E,1)/r! |
Ω |
0.39651628483864 |
Real period |
R |
1.4985152676365 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000289 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60192m1 120384cp1 6688b1 |
Quadratic twists by: -4 8 -3 |