Properties

Label 28224.bi
Number of curves $2$
Conductor $28224$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28224.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.bi1 28224dx2 \([0, 0, 0, -21756, 1234800]\) \(21882096/7\) \(364309069824\) \([2]\) \(49152\) \(1.1932\)  
28224.bi2 28224dx1 \([0, 0, 0, -1176, 24696]\) \(-55296/49\) \(-159385218048\) \([2]\) \(24576\) \(0.84666\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 28224.2.a.bi

sage: E.q_eigenform(10)
 
\(q - 2q^{5} - 2q^{11} + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.