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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 32487.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32487.j1 | 32487r2 | \([1, 0, 1, -16049, 260579]\) | \(3885442650361/1996623837\) | \(234900797799213\) | \([2]\) | \(207360\) | \(1.4497\) | |
32487.j2 | 32487r1 | \([1, 0, 1, -12864, 559969]\) | \(2000852317801/2094417\) | \(246406065633\) | \([2]\) | \(103680\) | \(1.1031\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32487.j have rank \(0\).
Complex multiplication
The elliptic curves in class 32487.j do not have complex multiplication.Modular form 32487.2.a.j
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.