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Properties

Label 143143.bf
Number of curves $2$
Conductor $143143$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 143143.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
143143.bf1 143143bf2 \([1, 1, 0, -1053549, -384664210]\) \(15124197817/1294139\) \(11066165220165066011\) \([2]\) \(3110400\) \(2.3954\)  
143143.bf2 143143bf1 \([1, 1, 0, 71146, -27686017]\) \(4657463/41503\) \(-354891595981970047\) \([2]\) \(1555200\) \(2.0488\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 143143.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 143143.bf do not have complex multiplication.

Modular form 143143.2.a.bf

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