Properties

Label 22848.br
Number of curves $2$
Conductor $22848$
CM no
Rank $0$
Graph

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

Elliptic curves in class 22848.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22848.br1 22848v1 \([0, 1, 0, -1349, -19509]\) \(265327034368/297381\) \(304518144\) \([2]\) \(11520\) \(0.54191\) \(\Gamma_0(N)\)-optimal
22848.br2 22848v2 \([0, 1, 0, -1009, -29233]\) \(-6940769488/18000297\) \(-294916866048\) \([2]\) \(23040\) \(0.88849\)  

Rank

sage: E.rank()
 

The elliptic curves in class 22848.br have rank \(0\).

Complex multiplication

The elliptic curves in class 22848.br do not have complex multiplication.

Modular form 22848.2.a.br

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} - q^{7} + q^{9} - 6 q^{13} - 2 q^{15} - q^{17} + 2 q^{19} + O(q^{20})\)  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.