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Properties

Label 286110.ez
Number of curves $2$
Conductor $286110$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ez1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 286110.ez

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286110.ez1 286110ez2 [1, -1, 1, -373298, -55981969] [2] 4718592  
286110.ez2 286110ez1 [1, -1, 1, 68872, -6105193] [2] 2359296 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 286110.ez have rank \(0\).

Complex multiplication

The elliptic curves in class 286110.ez do not have complex multiplication.

Modular form 286110.2.a.ez

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{5} + 2q^{7} + q^{8} - q^{10} + q^{11} + 2q^{14} + q^{16} + O(q^{20}) \)

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.