Properties

Label 61017a
Number of curves 4
Conductor 61017
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("61017.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 61017a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61017.a3 61017a1 [1, 0, 0, -12057, 504288] [2] 121968 \(\Gamma_0(N)\)-optimal
61017.a2 61017a2 [1, 0, 0, -21302, -377685] [2, 2] 243936  
61017.a4 61017a3 [1, 0, 0, 80393, -2920060] [2] 487872  
61017.a1 61017a4 [1, 0, 0, -270917, -54244602] [2] 487872  

Rank

sage: E.rank()
 

The elliptic curves in class 61017a have rank \(0\).

Modular form 61017.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} - q^{4} + 2q^{5} - q^{6} - 4q^{7} + 3q^{8} + q^{9} - 2q^{10} + q^{11} - q^{12} - 2q^{13} + 4q^{14} + 2q^{15} - q^{16} - 2q^{17} - q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.