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Properties

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

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

Elliptic curves in class 346560.io

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.io1 346560io2 \([0, 1, 0, -616496065, 5876559797663]\) \(306331959547531/900000000\) \(76131579461920358400000000\) \([2]\) \(224133120\) \(3.8364\)  
346560.io2 346560io1 \([0, 1, 0, -54606785, 7851023775]\) \(212883113611/122880000\) \(10394498315867526266880000\) \([2]\) \(112066560\) \(3.4898\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 346560.io do not have complex multiplication.

Modular form 346560.2.a.io

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