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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 230622.l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 230622.l1 | 230622l3 | \([1, 1, 0, -5245789, 4622307547]\) | \(661397832743623417/443352042\) | \(10701440505065898\) | \([2]\) | \(6553600\) | \(2.3919\) | |
| 230622.l2 | 230622l2 | \([1, 1, 0, -329899, 71176585]\) | \(164503536215257/4178071044\) | \(100848478111452036\) | \([2, 2]\) | \(3276800\) | \(2.0453\) | |
| 230622.l3 | 230622l1 | \([1, 1, 0, -46679, -2290683]\) | \(466025146777/177366672\) | \(4281200283700368\) | \([2]\) | \(1638400\) | \(1.6988\) | \(\Gamma_0(N)\)-optimal |
| 230622.l4 | 230622l4 | \([1, 1, 0, 54471, 227615175]\) | \(740480746823/927484650666\) | \(-22387224751891470954\) | \([2]\) | \(6553600\) | \(2.3919\) |
Rank
sage: E.rank()
The elliptic curves in class 230622.l have rank \(1\).
Complex multiplication
The elliptic curves in class 230622.l do not have complex multiplication.Modular form 230622.2.a.l
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.
