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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 206310.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
206310.bs1 | 206310u2 | \([1, 1, 1, -24345, 1299597]\) | \(10779215329/1232010\) | \(182381695606890\) | \([2]\) | \(1140480\) | \(1.4687\) | |
206310.bs2 | 206310u1 | \([1, 1, 1, 2105, 104057]\) | \(6967871/35100\) | \(-5196059703900\) | \([2]\) | \(570240\) | \(1.1221\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206310.bs have rank \(0\).
Complex multiplication
The elliptic curves in class 206310.bs do not have complex multiplication.Modular form 206310.2.a.bs
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.