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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 86190db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86190.da2 | 86190db1 | \([1, 0, 0, 380, -79600]\) | \(2761677827/1248480000\) | \(-2742910560000\) | \([2]\) | \(202752\) | \(1.0658\) | \(\Gamma_0(N)\)-optimal |
86190.da1 | 86190db2 | \([1, 0, 0, -25620, -1540800]\) | \(846509996114173/24354723600\) | \(53507327749200\) | \([2]\) | \(405504\) | \(1.4123\) |
Rank
sage: E.rank()
The elliptic curves in class 86190db have rank \(1\).
Complex multiplication
The elliptic curves in class 86190db do not have complex multiplication.Modular form 86190.2.a.db
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.