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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 283920k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.k1 | 283920k1 | \([0, -1, 0, -142016, 20523216]\) | \(64088267044/443625\) | \(2192684178048000\) | \([2]\) | \(1806336\) | \(1.7771\) | \(\Gamma_0(N)\)-optimal |
| 283920.k2 | 283920k2 | \([0, -1, 0, -54136, 45551440]\) | \(-1775007362/89578125\) | \(-885507071904000000\) | \([2]\) | \(3612672\) | \(2.1237\) |
Rank
sage: E.rank()
The elliptic curves in class 283920k have rank \(1\).
Complex multiplication
The elliptic curves in class 283920k do not have complex multiplication.Modular form 283920.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
