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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 132600bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 132600.ch1 | 132600bs1 | \([0, 1, 0, -77229883, -261255393262]\) | \(203769809659907949070336/2016474841511325\) | \(504118710377831250000\) | \([2]\) | \(12165120\) | \(3.1324\) | \(\Gamma_0(N)\)-optimal |
| 132600.ch2 | 132600bs2 | \([0, 1, 0, -75387508, -274310462512]\) | \(-11845731628994222232016/1269935194601506875\) | \(-5079740778406027500000000\) | \([2]\) | \(24330240\) | \(3.4790\) |
Rank
sage: E.rank()
The elliptic curves in class 132600bs have rank \(1\).
Complex multiplication
The elliptic curves in class 132600bs do not have complex multiplication.Modular form 132600.2.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.
