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Properties

Label 7350.bf
Number of curves $2$
Conductor $7350$
CM no
Rank $1$
Graph

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

Elliptic curves in class 7350.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.bf1 7350bf1 \([1, 0, 1, -44126, 3572048]\) \(-2637114025/6912\) \(-24903940320000\) \([3]\) \(36288\) \(1.4459\) \(\Gamma_0(N)\)-optimal
7350.bf2 7350bf2 \([1, 0, 1, 84499, 18183848]\) \(18519167975/50331648\) \(-181344959201280000\) \([]\) \(108864\) \(1.9952\)  

Rank

sage: E.rank()
 

The elliptic curves in class 7350.bf have rank \(1\).

Complex multiplication

The elliptic curves in class 7350.bf do not have complex multiplication.

Modular form 7350.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{12} + 5 q^{13} + q^{16} - 6 q^{17} - q^{18} - 7 q^{19} + O(q^{20})\) 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.