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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 273600ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 273600.ba2 | 273600ba1 | \([0, 0, 0, 16800, -169000]\) | \(44957696/27075\) | \(-315802800000000\) | \([2]\) | \(1179648\) | \(1.4714\) | \(\Gamma_0(N)\)-optimal |
| 273600.ba1 | 273600ba2 | \([0, 0, 0, -68700, -1366000]\) | \(192143824/106875\) | \(19945440000000000\) | \([2]\) | \(2359296\) | \(1.8180\) |
Rank
sage: E.rank()
The elliptic curves in class 273600ba have rank \(0\).
Complex multiplication
The elliptic curves in class 273600ba do not have complex multiplication.Modular form 273600.2.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.
