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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 382200j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
382200.j1 | 382200j1 | \([0, -1, 0, -443, 3732]\) | \(14047232/39\) | \(26754000\) | \([2]\) | \(143360\) | \(0.29785\) | \(\Gamma_0(N)\)-optimal |
382200.j2 | 382200j2 | \([0, -1, 0, -268, 6532]\) | \(-194672/1521\) | \(-16694496000\) | \([2]\) | \(286720\) | \(0.64443\) |
Rank
sage: E.rank()
The elliptic curves in class 382200j have rank \(2\).
Complex multiplication
The elliptic curves in class 382200j do not have complex multiplication.Modular form 382200.2.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 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.