Properties

Label 41616.be
Number of curves $4$
Conductor $41616$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 41616.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41616.be1 41616ca4 \([0, 0, 0, -4703475, -2713145294]\) \(159661140625/48275138\) \(3479401356824541339648\) \([2]\) \(1990656\) \(2.8385\)  
41616.be2 41616ca3 \([0, 0, 0, -4287315, -3416372462]\) \(120920208625/19652\) \(1416406007256072192\) \([2]\) \(995328\) \(2.4920\)  
41616.be3 41616ca2 \([0, 0, 0, -1790355, 921845842]\) \(8805624625/2312\) \(166636000853655552\) \([2]\) \(663552\) \(2.2892\)  
41616.be4 41616ca1 \([0, 0, 0, -125715, 10621906]\) \(3048625/1088\) \(78416941578190848\) \([2]\) \(331776\) \(1.9427\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 41616.be have rank \(1\).

Complex multiplication

The elliptic curves in class 41616.be do not have complex multiplication.

Modular form 41616.2.a.be

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