Properties

Label 42483.d
Number of curves 6
Conductor 42483
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("42483.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 42483.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
42483.d1 42483v6 [1, 0, 0, -11102519, 14238104670] [2] 884736  
42483.d2 42483v4 [1, 0, 0, -694184, 222240759] [2, 2] 442368  
42483.d3 42483v3 [1, 0, 0, -552574, -157189075] [2] 442368  
42483.d4 42483v5 [1, 0, 0, -481769, 360862788] [2] 884736  
42483.d5 42483v2 [1, 0, 0, -56939, 1116744] [2, 2] 221184  
42483.d6 42483v1 [1, 0, 0, 13866, 139635] [2] 110592 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 42483.d have rank \(1\).

Modular form 42483.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} - q^{4} - 2q^{5} - q^{6} + 3q^{8} + q^{9} + 2q^{10} - 4q^{11} - q^{12} + 2q^{13} - 2q^{15} - q^{16} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.