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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 58800be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 58800.ee3 | 58800be1 | \([0, -1, 0, -87383, -9500238]\) | \(2508888064/118125\) | \(3474322031250000\) | \([2]\) | \(442368\) | \(1.7428\) | \(\Gamma_0(N)\)-optimal |
| 58800.ee2 | 58800be2 | \([0, -1, 0, -240508, 33068512]\) | \(3269383504/893025\) | \(420253992900000000\) | \([2, 2]\) | \(884736\) | \(2.0894\) | |
| 58800.ee4 | 58800be3 | \([0, -1, 0, 616992, 214858512]\) | \(13799183324/18600435\) | \(-35013161237040000000\) | \([2]\) | \(1769472\) | \(2.4360\) | |
| 58800.ee1 | 58800be4 | \([0, -1, 0, -3548008, 2573228512]\) | \(2624033547076/324135\) | \(610146537840000000\) | \([2]\) | \(1769472\) | \(2.4360\) |
Rank
sage: E.rank()
The elliptic curves in class 58800be have rank \(0\).
Complex multiplication
The elliptic curves in class 58800be do not have complex multiplication.Modular form 58800.2.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 Cremona 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 Cremona labels.
