Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("dx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28224.dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.dx1 28224dm1 \([0, 0, 0, -85995, -9705528]\) \(474552000/49\) \(7261988997312\) \([2]\) \(73728\) \(1.5004\) \(\Gamma_0(N)\)-optimal
28224.dx2 28224dm2 \([0, 0, 0, -79380, -11261376]\) \(-5832000/2401\) \(-22773597495570432\) \([2]\) \(147456\) \(1.8470\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 28224.2.a.dx

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