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Properties

Label 160446.g
Number of curves $2$
Conductor $160446$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 160446.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.g1 160446bt2 \([1, 1, 0, -98027789, 373527674205]\) \(44181166128077784203/195126437376\) \(460097932463795298816\) \([2]\) \(26915328\) \(3.1706\)  
160446.g2 160446bt1 \([1, 1, 0, -6029069, 6029587293]\) \(-10278752783033483/717973880832\) \(-1692944854506123558912\) \([2]\) \(13457664\) \(2.8240\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 160446.g have rank \(1\).

Complex multiplication

The elliptic curves in class 160446.g do not have complex multiplication.

Modular form 160446.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 2 q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} - 2 q^{10} - q^{12} - q^{13} + 4 q^{14} - 2 q^{15} + q^{16} - q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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 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.