Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28224.co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.co1 28224bs2 \([0, 0, 0, -81228, -9244816]\) \(-6329617441/279936\) \(-2621333531787264\) \([]\) \(129024\) \(1.7235\)  
28224.co2 28224bs1 \([0, 0, 0, -588, 12656]\) \(-2401/6\) \(-56184274944\) \([]\) \(18432\) \(0.75055\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 28224.2.a.co

sage: E.q_eigenform(10)
 
\(q - q^{5} + 5 q^{11} - 4 q^{17} + 8 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.