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Properties

Label 20230.k
Number of curves $2$
Conductor $20230$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 20230.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20230.k1 20230k2 \([1, 0, 1, -31555483, 19608529318]\) \(498146195040339241/264461398835200\) \(1844818570781915132723200\) \([]\) \(3172608\) \(3.3476\)  
20230.k2 20230k1 \([1, 0, 1, -24800108, 47534512618]\) \(241820454028845241/343000000\) \(2392684802263000000\) \([3]\) \(1057536\) \(2.7983\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 20230.k do not have complex multiplication.

Modular form 20230.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} - 2 q^{9} - q^{10} + q^{12} + 2 q^{13} - q^{14} + q^{15} + q^{16} + 2 q^{18} + 5 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.