Properties

Label 60840y
Number of curves 4
Conductor 60840
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("60840.cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60840y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
60840.cb3 60840y1 [0, 0, 0, -3042, -59319] [2] 73728 \(\Gamma_0(N)\)-optimal
60840.cb2 60840y2 [0, 0, 0, -10647, 355914] [2, 2] 147456  
60840.cb4 60840y3 [0, 0, 0, 19773, 2016846] [2] 294912  
60840.cb1 60840y4 [0, 0, 0, -162747, 25269894] [2] 294912  

Rank

sage: E.rank()
 

The elliptic curves in class 60840y have rank \(1\).

Modular form 60840.2.a.cb

sage: E.q_eigenform(10)
 
\( q + q^{5} + 4q^{7} + 4q^{11} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.