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Properties

Label 489566y
Number of curves $2$
Conductor $489566$
CM no
Rank $1$
Graph

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 489566y have rank \(1\).

Complex multiplication

The elliptic curves in class 489566y do not have complex multiplication.

Modular form 489566.2.a.y

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 3 q^{9} - 2 q^{13} - q^{14} + q^{16} + 3 q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 489566y

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
489566.y1 489566y1 \([1, -1, 0, -26565512, -49778558912]\) \(9869198625/614656\) \(129130409635030851229952\) \([2]\) \(50135040\) \(3.1860\) \(\Gamma_0(N)\)-optimal
489566.y2 489566y2 \([1, -1, 0, 20992328, -208536140400]\) \(4869777375/92236816\) \(-19377632095856817112694672\) \([2]\) \(100270080\) \(3.5326\)