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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 85782q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
85782.o1 | 85782q1 | \([1, 0, 0, -2120, 23676]\) | \(1771561/612\) | \(364031872452\) | \([2]\) | \(198016\) | \(0.92012\) | \(\Gamma_0(N)\)-optimal |
85782.o2 | 85782q2 | \([1, 0, 0, 6290, 166646]\) | \(46268279/46818\) | \(-27848438242578\) | \([2]\) | \(396032\) | \(1.2667\) |
Rank
sage: E.rank()
The elliptic curves in class 85782q have rank \(0\).
Complex multiplication
The elliptic curves in class 85782q do not have complex multiplication.Modular form 85782.2.a.q
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.