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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 10608x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10608.l2 | 10608x1 | \([0, 1, 0, -4200, 103284]\) | \(2000852317801/2094417\) | \(8578732032\) | \([2]\) | \(18432\) | \(0.82332\) | \(\Gamma_0(N)\)-optimal |
| 10608.l1 | 10608x2 | \([0, 1, 0, -5240, 47124]\) | \(3885442650361/1996623837\) | \(8178171236352\) | \([2]\) | \(36864\) | \(1.1699\) |
Rank
sage: E.rank()
The elliptic curves in class 10608x have rank \(2\).
Complex multiplication
The elliptic curves in class 10608x do not have complex multiplication.Modular form 10608.2.a.x
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.
