Properties

Label 466752.bf
Number of curves $2$
Conductor $466752$
CM no
Rank $1$
Graph

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

Elliptic curves in class 466752.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
466752.bf1 466752bf1 \([0, -1, 0, -193313, 29820609]\) \(3047678972871625/304559880768\) \(79838545384046592\) \([2]\) \(4128768\) \(1.9796\) \(\Gamma_0(N)\)-optimal
466752.bf2 466752bf2 \([0, -1, 0, 239327, 143951041]\) \(5783051584712375/37533175779528\) \(-9839096831548588032\) \([2]\) \(8257536\) \(2.3262\)  

Rank

sage: E.rank()
 

The elliptic curves in class 466752.bf have rank \(1\).

Complex multiplication

The elliptic curves in class 466752.bf do not have complex multiplication.

Modular form 466752.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{7} + q^{9} + q^{11} - q^{13} - q^{17} + 4q^{19} + O(q^{20})\)  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.