Properties

Label 40432.l
Number of curves $4$
Conductor $40432$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40432.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40432.l1 40432j4 [0, 0, 0, -107939, 13649410] [2] 96768  
40432.l2 40432j3 [0, 0, 0, -21299, -946542] [2] 96768  
40432.l3 40432j2 [0, 0, 0, -6859, 205770] [2, 2] 48384  
40432.l4 40432j1 [0, 0, 0, 361, 13718] [2] 24192 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 40432.l have rank \(1\).

Complex multiplication

The elliptic curves in class 40432.l do not have complex multiplication.

Modular form 40432.2.a.l

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + q^{7} - 3q^{9} + 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.