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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 489566.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
489566.x1 | 489566x1 | \([1, -1, 0, -91922, -10110380]\) | \(9869198625/614656\) | \(5349768638052608\) | \([2]\) | \(2949120\) | \(1.7694\) | \(\Gamma_0(N)\)-optimal |
489566.x2 | 489566x2 | \([1, -1, 0, 72638, -42462876]\) | \(4869777375/92236816\) | \(-802799656247769488\) | \([2]\) | \(5898240\) | \(2.1160\) |
Rank
sage: E.rank()
The elliptic curves in class 489566.x have rank \(0\).
Complex multiplication
The elliptic curves in class 489566.x do not have complex multiplication.Modular form 489566.2.a.x
sage: E.q_eigenform(10)
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.