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SageMath
E = EllipticCurve("ee1")
E.isogeny_class()
Elliptic curves in class 203280ee
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 203280.u4 | 203280ee1 | \([0, -1, 0, -78371256, -285396973200]\) | \(-7336316844655213969/604492922880000\) | \(-4386390372148083425280000\) | \([2]\) | \(44236800\) | \(3.4742\) | \(\Gamma_0(N)\)-optimal |
| 203280.u3 | 203280ee2 | \([0, -1, 0, -1277761976, -17579651643024]\) | \(31794905164720991157649/192099600000000\) | \(1393934989212057600000000\) | \([2, 2]\) | \(88473600\) | \(3.8207\) | |
| 203280.u2 | 203280ee3 | \([0, -1, 0, -1301613496, -16889216923280]\) | \(33608860073906150870929/2466782226562500000\) | \(17899746050340000000000000000\) | \([2]\) | \(176947200\) | \(4.1673\) | |
| 203280.u1 | 203280ee4 | \([0, -1, 0, -20444161976, -1125121575483024]\) | \(130231365028993807856757649/4753980000\) | \(34496370945146880000\) | \([2]\) | \(176947200\) | \(4.1673\) |
Rank
sage: E.rank()
The elliptic curves in class 203280ee have rank \(1\).
Complex multiplication
The elliptic curves in class 203280ee do not have complex multiplication.Modular form 203280.2.a.ee
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.
