Properties

Label 5040.d
Number of curves 4
Conductor 5040
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("5040.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5040.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5040.d1 5040bd3 [0, 0, 0, -16203, -793798] [2] 8192  
5040.d2 5040bd2 [0, 0, 0, -1083, -10582] [2, 2] 4096  
5040.d3 5040bd1 [0, 0, 0, -363, 2522] [2] 2048 \(\Gamma_0(N)\)-optimal
5040.d4 5040bd4 [0, 0, 0, 2517, -66022] [2] 8192  

Rank

sage: E.rank()
 

The elliptic curves in class 5040.d have rank \(1\).

Modular form 5040.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{7} - 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.