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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 272832ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 272832.ba2 | 272832ba1 | \([0, -1, 0, -420289, 108491713]\) | \(-776151559/30276\) | \(-320273332445380608\) | \([2]\) | \(4128768\) | \(2.1281\) | \(\Gamma_0(N)\)-optimal |
| 272832.ba1 | 272832ba2 | \([0, -1, 0, -6786369, 6806881089]\) | \(3267487271719/4698\) | \(49697586069110784\) | \([2]\) | \(8257536\) | \(2.4747\) |
Rank
sage: E.rank()
The elliptic curves in class 272832ba have rank \(0\).
Complex multiplication
The elliptic curves in class 272832ba do not have complex multiplication.Modular form 272832.2.a.ba
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.
