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Properties

Label 293046.be
Number of curves $2$
Conductor $293046$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 293046.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
293046.be1 293046be2 \([1, 0, 1, -6355387302, -195012444329168]\) \(-843137281012581793/216\) \(-7272860140375726104\) \([]\) \(266499072\) \(3.9016\)  
293046.be2 293046be1 \([1, 0, 1, -78341982, -268368685232]\) \(-1579268174113/10077696\) \(-339322562709369877108224\) \([]\) \(88833024\) \(3.3523\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 293046.be have rank \(1\).

Complex multiplication

The elliptic curves in class 293046.be do not have complex multiplication.

Modular form 293046.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + 3 q^{5} - q^{6} + 4 q^{7} - q^{8} + q^{9} - 3 q^{10} - 3 q^{11} + q^{12} - 4 q^{14} + 3 q^{15} + q^{16} - q^{18} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.