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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 66270.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66270.y1 | 66270y2 | \([1, 0, 0, -495520, 133606400]\) | \(129602612829192047/680244480000\) | \(70625022647040000\) | \([2]\) | \(811008\) | \(2.0781\) | |
66270.y2 | 66270y1 | \([1, 0, 0, -14240, 4334592]\) | \(-3075827761007/76441190400\) | \(-7936353710899200\) | \([2]\) | \(405504\) | \(1.7315\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 66270.y have rank \(1\).
Complex multiplication
The elliptic curves in class 66270.y do not have complex multiplication.Modular form 66270.2.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 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.