Properties

Label 58443a
Number of curves $2$
Conductor $58443$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 58443a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58443.o2 58443a1 \([1, 1, 0, -10045, -412496]\) \(-63282696625/4032567\) \(-7143938427087\) \([2]\) \(130560\) \(1.2199\) \(\Gamma_0(N)\)-optimal
58443.o1 58443a2 \([1, 1, 0, -163110, -25423317]\) \(270902819202625/1004157\) \(1778925379077\) \([2]\) \(261120\) \(1.5664\)  

Rank

sage: E.rank()
 

The elliptic curves in class 58443a have rank \(2\).

Complex multiplication

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

Modular form 58443.2.a.a

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} - q^{7} - 3 q^{8} + q^{9} + q^{12} + 4 q^{13} - q^{14} - q^{16} - 6 q^{17} + q^{18} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.