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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 3450y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3450.u2 | 3450y1 | \([1, 0, 0, -313, -3883]\) | \(-217081801/285660\) | \(-4463437500\) | \([2]\) | \(3456\) | \(0.54449\) | \(\Gamma_0(N)\)-optimal |
3450.u1 | 3450y2 | \([1, 0, 0, -6063, -182133]\) | \(1577505447721/838350\) | \(13099218750\) | \([2]\) | \(6912\) | \(0.89107\) |
Rank
sage: E.rank()
The elliptic curves in class 3450y have rank \(0\).
Complex multiplication
The elliptic curves in class 3450y do not have complex multiplication.Modular form 3450.2.a.y
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.