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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 20280be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20280.bf3 | 20280be1 | \([0, 1, 0, -18815, 984738]\) | \(9538484224/26325\) | \(2033051950800\) | \([4]\) | \(64512\) | \(1.2346\) | \(\Gamma_0(N)\)-optimal |
| 20280.bf2 | 20280be2 | \([0, 1, 0, -26420, 105600]\) | \(1650587344/950625\) | \(1174652238240000\) | \([2, 2]\) | \(129024\) | \(1.5812\) | |
| 20280.bf1 | 20280be3 | \([0, 1, 0, -279920, -56881200]\) | \(490757540836/2142075\) | \(10587532174003200\) | \([2]\) | \(258048\) | \(1.9278\) | |
| 20280.bf4 | 20280be4 | \([0, 1, 0, 105400, 949248]\) | \(26198797244/15234375\) | \(-75298220400000000\) | \([2]\) | \(258048\) | \(1.9278\) |
Rank
sage: E.rank()
The elliptic curves in class 20280be have rank \(0\).
Complex multiplication
The elliptic curves in class 20280be do not have complex multiplication.Modular form 20280.2.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.
