Properties

Label 41616ci
Number of curves 6
Conductor 41616
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("41616.s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 41616ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
41616.s5 41616ci1 [0, 0, 0, -1415811, 601361026] [2] 884736 \(\Gamma_0(N)\)-optimal
41616.s4 41616ci2 [0, 0, 0, -4745091, -3281245310] [2, 2] 1769472  
41616.s6 41616ci3 [0, 0, 0, 9404349, -19108808894] [2] 3538944  
41616.s2 41616ci4 [0, 0, 0, -72163011, -235940487230] [2, 2] 3538944  
41616.s3 41616ci5 [0, 0, 0, -68417571, -261524089694] [2] 7077888  
41616.s1 41616ci6 [0, 0, 0, -1154595171, -15100548367646] [2] 7077888  

Rank

sage: E.rank()
 

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

Modular form 41616.2.a.s

sage: E.q_eigenform(10)
 
\( q - 2q^{5} + 4q^{11} - 2q^{13} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.