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Properties

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

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Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 7350.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.br1 7350bv2 \([1, 1, 1, -3438, 74031]\) \(838561807/26244\) \(140651437500\) \([2]\) \(10240\) \(0.91420\)  
7350.br2 7350bv1 \([1, 1, 1, 62, 4031]\) \(4913/1296\) \(-6945750000\) \([2]\) \(5120\) \(0.56763\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7350.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - 4 q^{11} - q^{12} + 4 q^{13} + q^{16} + q^{18} - 4 q^{19} + O(q^{20})\) 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.