Properties

Label 20230r
Number of curves $4$
Conductor $20230$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("20230.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20230r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20230.n4 20230r1 [1, -1, 1, 668, -10761] [2] 20480 \(\Gamma_0(N)\)-optimal
20230.n3 20230r2 [1, -1, 1, -5112, -112489] [2, 2] 40960  
20230.n1 20230r3 [1, -1, 1, -77362, -8262289] [2] 81920  
20230.n2 20230r4 [1, -1, 1, -25342, 1457359] [2] 81920  

Rank

sage: E.rank()
 

The elliptic curves in class 20230r have rank \(0\).

Modular form 20230.2.a.n

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} - 3q^{9} + q^{10} - 4q^{11} - 6q^{13} + q^{14} + q^{16} - 3q^{18} + O(q^{20}) \)

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 Cremona 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 Cremona labels.