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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 11760.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11760.bg1 | 11760bx3 | \([0, -1, 0, -292840, 61092592]\) | \(5763259856089/5670\) | \(2732318023680\) | \([2]\) | \(73728\) | \(1.6797\) | |
| 11760.bg2 | 11760bx2 | \([0, -1, 0, -18440, 944112]\) | \(1439069689/44100\) | \(21251362406400\) | \([2, 2]\) | \(36864\) | \(1.3331\) | |
| 11760.bg3 | 11760bx1 | \([0, -1, 0, -2760, -34320]\) | \(4826809/1680\) | \(809575710720\) | \([2]\) | \(18432\) | \(0.98654\) | \(\Gamma_0(N)\)-optimal |
| 11760.bg4 | 11760bx4 | \([0, -1, 0, 5080, 3164400]\) | \(30080231/9003750\) | \(-4338819824640000\) | \([2]\) | \(73728\) | \(1.6797\) |
Rank
sage: E.rank()
The elliptic curves in class 11760.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 11760.bg do not have complex multiplication.Modular form 11760.2.a.bg
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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
