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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 11616ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11616.bd3 | 11616ba1 | \([0, 1, 0, -282, -1080]\) | \(21952/9\) | \(1020419136\) | \([2, 2]\) | \(5120\) | \(0.42615\) | \(\Gamma_0(N)\)-optimal |
| 11616.bd1 | 11616ba2 | \([0, 1, 0, -3912, -95460]\) | \(7301384/3\) | \(2721117696\) | \([2]\) | \(10240\) | \(0.77273\) | |
| 11616.bd2 | 11616ba3 | \([0, 1, 0, -2097, 35583]\) | \(140608/3\) | \(21768941568\) | \([2]\) | \(10240\) | \(0.77273\) | |
| 11616.bd4 | 11616ba4 | \([0, 1, 0, 928, -6888]\) | \(97336/81\) | \(-73470177792\) | \([2]\) | \(10240\) | \(0.77273\) |
Rank
sage: E.rank()
The elliptic curves in class 11616ba have rank \(0\).
Complex multiplication
The elliptic curves in class 11616ba do not have complex multiplication.Modular form 11616.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
