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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 110466w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110466.y1 | 110466w1 | \([1, -1, 0, -8190, 183168]\) | \(1771561/612\) | \(20989425716388\) | \([2]\) | \(442368\) | \(1.2580\) | \(\Gamma_0(N)\)-optimal |
110466.y2 | 110466w2 | \([1, -1, 0, 24300, 1255338]\) | \(46268279/46818\) | \(-1605691067303682\) | \([2]\) | \(884736\) | \(1.6046\) |
Rank
sage: E.rank()
The elliptic curves in class 110466w have rank \(0\).
Complex multiplication
The elliptic curves in class 110466w do not have complex multiplication.Modular form 110466.2.a.w
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.