Properties

Label 229320.n
Number of curves $4$
Conductor $229320$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.n1 229320dq3 \([0, 0, 0, -596239203, 5603751974702]\) \(266912903848829942596/152163375\) \(13363673530386816000\) \([2]\) \(33030144\) \(3.4309\)  
229320.n2 229320dq2 \([0, 0, 0, -37271703, 87525304202]\) \(260798860029250384/196803140625\) \(4321034744838084000000\) \([2, 2]\) \(16515072\) \(3.0843\)  
229320.n3 229320dq4 \([0, 0, 0, -29554203, 124811633702]\) \(-32506165579682596/57814914850875\) \(-5077566446289758418816000\) \([2]\) \(33030144\) \(3.4309\)  
229320.n4 229320dq1 \([0, 0, 0, -2818578, 751663577]\) \(1804588288006144/866455078125\) \(1188999857144531250000\) \([2]\) \(8257536\) \(2.7377\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 229320.n have rank \(0\).

Complex multiplication

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

Modular form 229320.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.