Atkin-Lehner |
2+ 3- 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
60192f |
Isogeny class |
Conductor |
60192 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
101376 |
Modular degree for the optimal curve |
Δ |
-675868520448 = -1 · 212 · 37 · 11 · 193 |
Discriminant |
Eigenvalues |
2+ 3- -2 2 11+ 7 7 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-7176,237296] |
[a1,a2,a3,a4,a6] |
Generators |
[-44:684:1] |
Generators of the group modulo torsion |
j |
-13686220288/226347 |
j-invariant |
L |
6.6668866304147 |
L(r)(E,1)/r! |
Ω |
0.90904060978543 |
Real period |
R |
0.61116508975472 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999584 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
60192w1 120384bl1 20064r1 |
Quadratic twists by: -4 8 -3 |