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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 237160.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 237160.be1 | 237160be4 | \([0, 0, 0, -634403, -194483058]\) | \(132304644/5\) | \(1067122586055680\) | \([2]\) | \(1474560\) | \(1.9697\) | |
| 237160.be2 | 237160be2 | \([0, 0, 0, -41503, -2739198]\) | \(148176/25\) | \(1333903232569600\) | \([2, 2]\) | \(737280\) | \(1.6231\) | |
| 237160.be3 | 237160be1 | \([0, 0, 0, -11858, 456533]\) | \(55296/5\) | \(16673790407120\) | \([2]\) | \(368640\) | \(1.2765\) | \(\Gamma_0(N)\)-optimal |
| 237160.be4 | 237160be3 | \([0, 0, 0, 77077, -15522122]\) | \(237276/625\) | \(-133390323256960000\) | \([2]\) | \(1474560\) | \(1.9697\) |
Rank
sage: E.rank()
The elliptic curves in class 237160.be have rank \(0\).
Complex multiplication
The elliptic curves in class 237160.be do not have complex multiplication.Modular form 237160.2.a.be
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.
