Properties

Label 1560.l
Number of curves $4$
Conductor $1560$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1560.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1560.l1 1560h3 \([0, 1, 0, -561600, -162177552]\) \(19129597231400697604/26325\) \(26956800\) \([2]\) \(6144\) \(1.5921\)  
1560.l2 1560h2 \([0, 1, 0, -35100, -2542752]\) \(18681746265374416/693005625\) \(177409440000\) \([2, 2]\) \(3072\) \(1.2455\)  
1560.l3 1560h4 \([0, 1, 0, -33480, -2786400]\) \(-4053153720264484/903687890625\) \(-925376400000000\) \([4]\) \(6144\) \(1.5921\)  
1560.l4 1560h1 \([0, 1, 0, -2295, -36450]\) \(83587439220736/13990184325\) \(223842949200\) \([4]\) \(1536\) \(0.89895\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1560.l have rank \(0\).

Complex multiplication

The elliptic curves in class 1560.l do not have complex multiplication.

Modular form 1560.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.