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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 89232bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 89232.a2 | 89232bs1 | \([0, -1, 0, -2760, 973296]\) | \(-117649/20592\) | \(-407116394201088\) | \([2]\) | \(645120\) | \(1.4827\) | \(\Gamma_0(N)\)-optimal |
| 89232.a1 | 89232bs2 | \([0, -1, 0, -165000, 25633776]\) | \(25128011089/245388\) | \(4851470364229632\) | \([2]\) | \(1290240\) | \(1.8293\) |
Rank
sage: E.rank()
The elliptic curves in class 89232bs have rank \(1\).
Complex multiplication
The elliptic curves in class 89232bs do not have complex multiplication.Modular form 89232.2.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.
