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Properties

Label 226350br
Number of curves $2$
Conductor $226350$
CM no
Rank $1$
Graph

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

Elliptic curves in class 226350br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
226350.j2 226350br1 \([1, -1, 0, 1758, -7084]\) \(52734375/32192\) \(-366687000000\) \([2]\) \(290304\) \(0.90817\) \(\Gamma_0(N)\)-optimal
226350.j1 226350br2 \([1, -1, 0, -7242, -52084]\) \(3687953625/2024072\) \(23055445125000\) \([2]\) \(580608\) \(1.2547\)  

Rank

sage: E.rank()
 

The elliptic curves in class 226350br have rank \(1\).

Complex multiplication

The elliptic curves in class 226350br do not have complex multiplication.

Modular form 226350.2.a.br

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