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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 389376j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
389376.j2 | 389376j1 | \([0, 0, 0, -303186, -103962040]\) | \(-778688/729\) | \(-2885460864658684416\) | \([2]\) | \(5271552\) | \(2.2386\) | \(\Gamma_0(N)\)-optimal |
389376.j1 | 389376j2 | \([0, 0, 0, -5641896, -5156517184]\) | \(78402752/27\) | \(6839610938450214912\) | \([2]\) | \(10543104\) | \(2.5852\) |
Rank
sage: E.rank()
The elliptic curves in class 389376j have rank \(0\).
Complex multiplication
The elliptic curves in class 389376j do not have complex multiplication.Modular form 389376.2.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.