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SageMath
E = EllipticCurve("ke1")
E.isogeny_class()
Elliptic curves in class 369600.ke
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.ke1 | 369600ke2 | \([0, -1, 0, -17953, 125377]\) | \(19530306557/11114334\) | \(364194496512000\) | \([2]\) | \(1179648\) | \(1.4839\) | |
| 369600.ke2 | 369600ke1 | \([0, -1, 0, 4447, 13377]\) | \(296740963/174636\) | \(-5722472448000\) | \([2]\) | \(589824\) | \(1.1373\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.ke have rank \(1\).
Complex multiplication
The elliptic curves in class 369600.ke do not have complex multiplication.Modular form 369600.2.a.ke
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
