Properties

Label 346560.io
Number of curves $2$
Conductor $346560$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("346560.io1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 346560.io

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
346560.io1 346560io2 [0, 1, 0, -616496065, 5876559797663] [2] 224133120  
346560.io2 346560io1 [0, 1, 0, -54606785, 7851023775] [2] 112066560 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 346560.io have rank \(1\).

Modular form 346560.2.a.io

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - 4q^{7} + q^{9} - 6q^{11} - 4q^{13} + q^{15} + 6q^{17} + O(q^{20}) \)

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.