Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 229320.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.cv1 229320cu3 \([0, 0, 0, -3669267, 2705310286]\) \(31103978031362/195\) \(34251558082560\) \([2]\) \(3538944\) \(2.2026\)  
229320.cv2 229320cu4 \([0, 0, 0, -317667, 6778366]\) \(20183398562/11567205\) \(2031768173899376640\) \([2]\) \(3538944\) \(2.2026\)  
229320.cv3 229320cu2 \([0, 0, 0, -229467, 42217126]\) \(15214885924/38025\) \(3339526913049600\) \([2, 2]\) \(1769472\) \(1.8561\)  
229320.cv4 229320cu1 \([0, 0, 0, -8967, 1160026]\) \(-3631696/24375\) \(-535180595040000\) \([2]\) \(884736\) \(1.5095\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 229320.2.a.cv

sage: E.q_eigenform(10)
 
\(q + q^{5} - 4q^{11} - q^{13} + 6q^{17} + O(q^{20})\)  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.