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Properties

Label 247962bb
Number of curves $2$
Conductor $247962$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 247962bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
247962.bb2 247962bb1 \([1, 0, 0, -664995, -209693439]\) \(-1347365318848849/6831931392\) \(-164906215377666048\) \([2]\) \(5971968\) \(2.1505\) \(\Gamma_0(N)\)-optimal
247962.bb1 247962bb2 \([1, 0, 0, -10652835, -13383654399]\) \(5538928862777598289/141343488\) \(3411688194300672\) \([2]\) \(11943936\) \(2.4971\)  

Rank

sage: E.rank()
 

The elliptic curves in class 247962bb have rank \(0\).

Complex multiplication

The elliptic curves in class 247962bb do not have complex multiplication.

Modular form 247962.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 4 q^{5} + q^{6} + q^{8} + q^{9} - 4 q^{10} - q^{11} + q^{12} + q^{13} - 4 q^{15} + q^{16} + q^{18} + O(q^{20})\) 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 Cremona 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 Cremona labels.