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Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 1560b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1560.e2 1560b1 \([0, -1, 0, 720, -8100]\) \(40254822716/49359375\) \(-50544000000\) \([2]\) \(960\) \(0.73996\) \(\Gamma_0(N)\)-optimal
1560.e1 1560b2 \([0, -1, 0, -4280, -74100]\) \(4234737878642/1247410125\) \(2554695936000\) \([2]\) \(1920\) \(1.0865\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1560.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 2 q^{7} + q^{9} + 4 q^{11} - q^{13} - q^{15} + 2 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.