Properties

Label 4032.u
Number of curves 4
Conductor 4032
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4032.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4032.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4032.u1 4032n4 [0, 0, 0, -65820, 6499568] [2] 9216  
4032.u2 4032n3 [0, 0, 0, -4080, 103304] [2] 4608  
4032.u3 4032n2 [0, 0, 0, -1020, 4016] [2] 3072  
4032.u4 4032n1 [0, 0, 0, 240, 488] [2] 1536 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4032.u have rank \(1\).

Modular form 4032.2.a.u

sage: E.q_eigenform(10)
 
\( q + q^{7} - 6q^{11} - 2q^{13} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.