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SageMath
E = EllipticCurve("ht1")
E.isogeny_class()
Elliptic curves in class 100800ht
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.kj1 | 100800ht1 | \([0, 0, 0, -2455500, -1473050000]\) | \(4386781853/27216\) | \(10158317568000000000\) | \([2]\) | \(2457600\) | \(2.4851\) | \(\Gamma_0(N)\)-optimal |
100800.kj2 | 100800ht2 | \([0, 0, 0, -1015500, -3186650000]\) | \(-310288733/11573604\) | \(-4319824545792000000000\) | \([2]\) | \(4915200\) | \(2.8317\) |
Rank
sage: E.rank()
The elliptic curves in class 100800ht have rank \(0\).
Complex multiplication
The elliptic curves in class 100800ht do not have complex multiplication.Modular form 100800.2.a.ht
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.