Properties

Label 16560.m
Number of curves $4$
Conductor $16560$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("m1")
 
E.isogeny_class()
 

Elliptic curves in class 16560.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16560.m1 16560bp3 \([0, 0, 0, -212043, -37582342]\) \(353108405631241/172500\) \(515082240000\) \([2]\) \(49152\) \(1.5824\)  
16560.m2 16560bp2 \([0, 0, 0, -13323, -580678]\) \(87587538121/1904400\) \(5686507929600\) \([2, 2]\) \(24576\) \(1.2358\)  
16560.m3 16560bp1 \([0, 0, 0, -1803, 16058]\) \(217081801/88320\) \(263722106880\) \([2]\) \(12288\) \(0.88923\) \(\Gamma_0(N)\)-optimal
16560.m4 16560bp4 \([0, 0, 0, 1077, -1770118]\) \(46268279/453342420\) \(-1353673212641280\) \([2]\) \(49152\) \(1.5824\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16560.m have rank \(0\).

Complex multiplication

The elliptic curves in class 16560.m do not have complex multiplication.

Modular form 16560.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{11} - 2 q^{13} - 2 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.