Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ge1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28224.ge

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.ge1 28224ct2 \([0, 0, 0, -3881388, 2862568240]\) \(838561807/26244\) \(202385707572063633408\) \([2]\) \(1376256\) \(2.6715\)  
28224.ge2 28224ct1 \([0, 0, 0, 69972, 151935280]\) \(4913/1296\) \(-9994355929484623872\) \([2]\) \(688128\) \(2.3249\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 28224.2.a.ge

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