Properties

Label 4560.a
Number of curves $4$
Conductor $4560$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.a1 4560q4 \([0, -1, 0, -19735096, 33751275376]\) \(207530301091125281552569/805586668007040\) \(3299682992156835840\) \([2]\) \(215040\) \(2.7666\)  
4560.a2 4560q3 \([0, -1, 0, -3740216, -2148427920]\) \(1412712966892699019449/330160465517040000\) \(1352337266757795840000\) \([2]\) \(215040\) \(2.7666\)  
4560.a3 4560q2 \([0, -1, 0, -1251896, 511088496]\) \(52974743974734147769/3152005008998400\) \(12910612516857446400\) \([2, 2]\) \(107520\) \(2.4200\)  
4560.a4 4560q1 \([0, -1, 0, 58824, 32937840]\) \(5495662324535111/117739817533440\) \(-482262292616970240\) \([2]\) \(53760\) \(2.0734\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4560.a have rank \(1\).

Complex multiplication

The elliptic curves in class 4560.a do not have complex multiplication.

Modular form 4560.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 4 q^{7} + q^{9} + 2 q^{13} + q^{15} - 2 q^{17} + q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.