Properties

Label 34650.bf
Number of curves $2$
Conductor $34650$
CM no
Rank $0$
Graph

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

Elliptic curves in class 34650.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34650.bf1 34650bz2 \([1, -1, 0, -63117, 802791]\) \(19530306557/11114334\) \(15824901339843750\) \([2]\) \(245760\) \(1.7982\)  
34650.bf2 34650bz1 \([1, -1, 0, 15633, 94041]\) \(296740963/174636\) \(-248651648437500\) \([2]\) \(122880\) \(1.4516\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 34650.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 34650.bf do not have complex multiplication.

Modular form 34650.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - q^{11} - 2 q^{13} - q^{14} + q^{16} + 2 q^{17} - 6 q^{19} + O(q^{20})\) 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.