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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 86640bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
86640.f2 | 86640bs1 | \([0, -1, 0, 66304, 9698880]\) | \(24389/45\) | \(-59477796454625280\) | \([2]\) | \(778240\) | \(1.9034\) | \(\Gamma_0(N)\)-optimal |
86640.f1 | 86640bs2 | \([0, -1, 0, -482416, 102322816]\) | \(9393931/2025\) | \(2676500840458137600\) | \([2]\) | \(1556480\) | \(2.2500\) |
Rank
sage: E.rank()
The elliptic curves in class 86640bs have rank \(0\).
Complex multiplication
The elliptic curves in class 86640bs do not have complex multiplication.Modular form 86640.2.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 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.