Properties

Label 28224.br
Number of curves $4$
Conductor $28224$
CM no
Rank $1$
Graph

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

Elliptic curves in class 28224.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.br1 28224ce4 \([0, 0, 0, -7113036, 7301811440]\) \(7080974546692/189\) \(1062325247606784\) \([2]\) \(589824\) \(2.3970\)  
28224.br2 28224ce3 \([0, 0, 0, -692076, -26578384]\) \(6522128932/3720087\) \(20909747848644329472\) \([2]\) \(589824\) \(2.3970\)  
28224.br3 28224ce2 \([0, 0, 0, -445116, 113793680]\) \(6940769488/35721\) \(50194867949420544\) \([2, 2]\) \(294912\) \(2.0504\)  
28224.br4 28224ce1 \([0, 0, 0, -12936, 3674216]\) \(-2725888/64827\) \(-5693399373892608\) \([2]\) \(147456\) \(1.7039\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28224.br have rank \(1\).

Complex multiplication

The elliptic curves in class 28224.br do not have complex multiplication.

Modular form 28224.2.a.br

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.