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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 272832bb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 272832.bb2 | 272832bb1 | \([0, -1, 0, -17509, -883931]\) | \(4927700992/12789\) | \(1540723774464\) | \([2]\) | \(589824\) | \(1.2143\) | \(\Gamma_0(N)\)-optimal |
| 272832.bb1 | 272832bb2 | \([0, -1, 0, -24369, -119727]\) | \(830321872/476847\) | \(919151783165952\) | \([2]\) | \(1179648\) | \(1.5608\) |
Rank
sage: E.rank()
The elliptic curves in class 272832bb have rank \(0\).
Complex multiplication
The elliptic curves in class 272832bb do not have complex multiplication.Modular form 272832.2.a.bb
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.
