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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 116160.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116160.bj1 | 116160fc6 | \([0, -1, 0, -1324882401, -18561102495615]\) | \(553808571467029327441/12529687500\) | \(5818838081126400000000\) | \([2]\) | \(35389440\) | \(3.7004\) | |
| 116160.bj2 | 116160fc4 | \([0, -1, 0, -91572961, 336578381185]\) | \(182864522286982801/463015182960\) | \(215026143209665478000640\) | \([2]\) | \(17694720\) | \(3.3539\) | |
| 116160.bj3 | 116160fc3 | \([0, -1, 0, -82899681, -289301115519]\) | \(135670761487282321/643043610000\) | \(298632080464336650240000\) | \([2, 2]\) | \(17694720\) | \(3.3539\) | |
| 116160.bj4 | 116160fc5 | \([0, -1, 0, -40307681, -586226984319]\) | \(-15595206456730321/310672490129100\) | \(-144277574067315939763814400\) | \([2]\) | \(35389440\) | \(3.7004\) | |
| 116160.bj5 | 116160fc2 | \([0, -1, 0, -7937761, 816507265]\) | \(119102750067601/68309049600\) | \(31723001798570960486400\) | \([2, 2]\) | \(8847360\) | \(3.0073\) | |
| 116160.bj6 | 116160fc1 | \([0, -1, 0, 1974559, 100837761]\) | \(1833318007919/1070530560\) | \(-497158767091164119040\) | \([2]\) | \(4423680\) | \(2.6607\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116160.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 116160.bj do not have complex multiplication.Modular form 116160.2.a.bj
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.
