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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 382200k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 382200.k4 | 382200k1 | \([0, -1, 0, 59617, -716988]\) | \(796706816/468195\) | \(-13770668388750000\) | \([2]\) | \(2949120\) | \(1.7862\) | \(\Gamma_0(N)\)-optimal |
| 382200.k3 | 382200k2 | \([0, -1, 0, -240508, -5518988]\) | \(3269383504/1863225\) | \(876826232100000000\) | \([2, 2]\) | \(5898240\) | \(2.1327\) | |
| 382200.k2 | 382200k3 | \([0, -1, 0, -2470008, 1488246012]\) | \(885341342596/4606875\) | \(8671907790000000000\) | \([2]\) | \(11796480\) | \(2.4793\) | |
| 382200.k1 | 382200k4 | \([0, -1, 0, -2813008, -1811413988]\) | \(1307761493476/2998905\) | \(5645090789520000000\) | \([2]\) | \(11796480\) | \(2.4793\) |
Rank
sage: E.rank()
The elliptic curves in class 382200k have rank \(0\).
Complex multiplication
The elliptic curves in class 382200k do not have complex multiplication.Modular form 382200.2.a.k
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.
