Properties

Label 230115.y
Number of curves 2
Conductor 230115
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("230115.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 230115.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
230115.y1 230115y1 [1, 0, 1, -197593, -33820969] [2] 912384 \(\Gamma_0(N)\)-optimal
230115.y2 230115y2 [1, 0, 1, -184368, -38539649] [2] 1824768  

Rank

sage: E.rank()
 

The elliptic curves in class 230115.y have rank \(1\).

Modular form 230115.2.a.y

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 3q^{8} + q^{9} + q^{10} - 2q^{11} - q^{12} + 2q^{13} + q^{15} - q^{16} + 4q^{17} + q^{18} + O(q^{20}) \)

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.