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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 87120.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 87120.bg1 | 87120ed6 | \([0, 0, 0, -2980985403, 62645211415402]\) | \(553808571467029327441/12529687500\) | \(66280202517830400000000\) | \([2]\) | \(35389440\) | \(3.9032\) | |
| 87120.bg2 | 87120ed4 | \([0, 0, 0, -206039163, -1135849016918]\) | \(182864522286982801/463015182960\) | \(2449282162497595835351040\) | \([2]\) | \(17694720\) | \(3.5566\) | |
| 87120.bg3 | 87120ed3 | \([0, 0, 0, -186524283, 976484527018]\) | \(135670761487282321/643043610000\) | \(3401606041539084656640000\) | \([2, 2]\) | \(17694720\) | \(3.5566\) | |
| 87120.bg4 | 87120ed5 | \([0, 0, 0, -90692283, 1978561418218]\) | \(-15595206456730321/310672490129100\) | \(-1643411742110520626372198400\) | \([2]\) | \(35389440\) | \(3.9032\) | |
| 87120.bg5 | 87120ed2 | \([0, 0, 0, -17859963, -2746782038]\) | \(119102750067601/68309049600\) | \(361344817361847346790400\) | \([2, 2]\) | \(8847360\) | \(3.2100\) | |
| 87120.bg6 | 87120ed1 | \([0, 0, 0, 4442757, -342548822]\) | \(1833318007919/1070530560\) | \(-5662949081397791293440\) | \([2]\) | \(4423680\) | \(2.8634\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 87120.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 87120.bg do not have complex multiplication.Modular form 87120.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
