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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 485100k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
485100.k1 | 485100k1 | \([0, 0, 0, -2101012200, 37067301876500]\) | \(-1647408715474378752/3025\) | \(-1883360486700000000\) | \([]\) | \(107993088\) | \(3.6531\) | \(\Gamma_0(N)\)-optimal |
485100.k2 | 485100k2 | \([0, 0, 0, -2094838200, 37295977918500]\) | \(-2239956387422208/27680640625\) | \(-12563531728581097687500000000\) | \([]\) | \(323979264\) | \(4.2024\) |
Rank
sage: E.rank()
The elliptic curves in class 485100k have rank \(0\).
Complex multiplication
The elliptic curves in class 485100k do not have complex multiplication.Modular form 485100.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.