Properties

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

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 60840y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
60840.cb3 60840y1 \([0, 0, 0, -3042, -59319]\) \(55296/5\) \(281499500880\) \([2]\) \(73728\) \(0.93642\) \(\Gamma_0(N)\)-optimal
60840.cb2 60840y2 \([0, 0, 0, -10647, 355914]\) \(148176/25\) \(22519960070400\) \([2, 2]\) \(147456\) \(1.2830\)  
60840.cb4 60840y3 \([0, 0, 0, 19773, 2016846]\) \(237276/625\) \(-2251996007040000\) \([2]\) \(294912\) \(1.6296\)  
60840.cb1 60840y4 \([0, 0, 0, -162747, 25269894]\) \(132304644/5\) \(18015968056320\) \([2]\) \(294912\) \(1.6296\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 60840y do not have complex multiplication.

Modular form 60840.2.a.y

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