Properties

Label 1560.k
Number of curves $2$
Conductor $1560$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1560.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1560.k1 1560g2 \([0, 1, 0, -200, 1008]\) \(434163602/7605\) \(15575040\) \([2]\) \(384\) \(0.17662\)  
1560.k2 1560g1 \([0, 1, 0, 0, 48]\) \(-4/975\) \(-998400\) \([2]\) \(192\) \(-0.16996\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1560.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - 2q^{7} + q^{9} + q^{13} + q^{15} - 4q^{17} + 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.