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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 28224bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28224.co2 | 28224bs1 | \([0, 0, 0, -588, 12656]\) | \(-2401/6\) | \(-56184274944\) | \([]\) | \(18432\) | \(0.75055\) | \(\Gamma_0(N)\)-optimal |
| 28224.co1 | 28224bs2 | \([0, 0, 0, -81228, -9244816]\) | \(-6329617441/279936\) | \(-2621333531787264\) | \([]\) | \(129024\) | \(1.7235\) |
Rank
sage: E.rank()
The elliptic curves in class 28224bs have rank \(1\).
Complex multiplication
The elliptic curves in class 28224bs do not have complex multiplication.Modular form 28224.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
