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Properties

Label 58443.k
Number of curves $2$
Conductor $58443$
CM no
Rank $1$
Graph

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

Elliptic curves in class 58443.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58443.k1 58443n2 [0, 1, 1, -85169, 9538139] [] 186624  
58443.k2 58443n1 [0, 1, 1, -2009, -14866] [] 62208 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 58443.k have rank \(1\).

Complex multiplication

The elliptic curves in class 58443.k do not have complex multiplication.

Modular form 58443.2.a.k

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{4} + 3q^{5} - q^{7} + q^{9} - 2q^{12} - 2q^{13} + 3q^{15} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20}) \)

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 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.