Properties

Label 486720.oy
Number of curves $2$
Conductor $486720$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("oy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 486720.oy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
486720.oy1 486720oy2 \([0, 0, 0, -4479852, -3269382064]\) \(10779215329/1232010\) \(1136427663619420323840\) \([2]\) \(24772608\) \(2.7725\) \(\Gamma_0(N)\)-optimal*
486720.oy2 486720oy1 \([0, 0, 0, 387348, -257558704]\) \(6967871/35100\) \(-32376856513373798400\) \([2]\) \(12386304\) \(2.4259\) \(\Gamma_0(N)\)-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 486720.oy1.

Rank

sage: E.rank()
 

The elliptic curves in class 486720.oy have rank \(0\).

Complex multiplication

The elliptic curves in class 486720.oy do not have complex multiplication.

Modular form 486720.2.a.oy

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2q^{7} + 4q^{11} - 8q^{17} + 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.