Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("eb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28224.eb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.eb1 28224en2 \([0, 0, 0, -3980172, -3170971888]\) \(-6329617441/279936\) \(-308397268681239822336\) \([]\) \(903168\) \(2.6965\)  
28224.eb2 28224en1 \([0, 0, 0, -28812, 4341008]\) \(-2401/6\) \(-6610023762886656\) \([]\) \(129024\) \(1.7235\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 28224.2.a.eb

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