Properties

Label 28224.cu
Number of curves $2$
Conductor $28224$
CM no
Rank $1$
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Show commands: SageMath
sage: E = EllipticCurve("cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28224.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.cu1 28224dn1 \([0, 0, 0, -9555, 359464]\) \(474552000/49\) \(9961576128\) \([2]\) \(24576\) \(0.95109\) \(\Gamma_0(N)\)-optimal
28224.cu2 28224dn2 \([0, 0, 0, -8820, 417088]\) \(-5832000/2401\) \(-31239502737408\) \([2]\) \(49152\) \(1.2977\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 28224.2.a.cu

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.