Properties

Label 229320.ci
Number of curves $4$
Conductor $229320$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.ci1 229320bw4 \([0, 0, 0, -5510883, -4979404402]\) \(210751929444676/1404585\) \(123356986434339840\) \([2]\) \(4718592\) \(2.4618\)  
229320.ci2 229320bw3 \([0, 0, 0, -1153803, 389481302]\) \(1934207124196/373156875\) \(32772318917869440000\) \([2]\) \(4718592\) \(2.4618\)  
229320.ci3 229320bw2 \([0, 0, 0, -351183, -74593582]\) \(218156637904/16769025\) \(368182842163718400\) \([2, 2]\) \(2359296\) \(2.1152\)  
229320.ci4 229320bw1 \([0, 0, 0, 21462, -5207083]\) \(796706816/8996715\) \(-12345813556680240\) \([2]\) \(1179648\) \(1.7686\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 229320.ci have rank \(1\).

Complex multiplication

The elliptic curves in class 229320.ci do not have complex multiplication.

Modular form 229320.2.a.ci

sage: E.q_eigenform(10)
 
\(q - q^{5} + 4 q^{11} + q^{13} - 2 q^{17} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.