Atkin-Lehner |
2+ 3+ 17+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
75072f |
Isogeny class |
Conductor |
75072 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
564224 |
Modular degree for the optimal curve |
Δ |
-14891228646506496 = -1 · 215 · 319 · 17 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ -3 -4 2 -2 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-39777,-6604479] |
[a1,a2,a3,a4,a6] |
Generators |
[1559:60976:1] |
Generators of the group modulo torsion |
j |
-212412842820296/454444233597 |
j-invariant |
L |
2.1360199458636 |
L(r)(E,1)/r! |
Ω |
0.15841609816424 |
Real period |
R |
6.7418020338909 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001189 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
75072bm1 37536z1 |
Quadratic twists by: -4 8 |