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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 111573y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111573.g2 | 111573y1 | \([1, -1, 1, 463, -4840]\) | \(43986977/64009\) | \(-16005258423\) | \([2]\) | \(110592\) | \(0.64351\) | \(\Gamma_0(N)\)-optimal |
111573.g1 | 111573y2 | \([1, -1, 1, -3002, -46420]\) | \(11961853903/3078251\) | \(769707427797\) | \([2]\) | \(221184\) | \(0.99009\) |
Rank
sage: E.rank()
The elliptic curves in class 111573y have rank \(1\).
Complex multiplication
The elliptic curves in class 111573y do not have complex multiplication.Modular form 111573.2.a.y
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 Cremona 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 Cremona labels.