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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 450840.by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 450840.by1 | 450840by1 | \([0, 1, 0, -28235396, -56029337856]\) | \(402876451435348816/13746755117745\) | \(84944192046252303847680\) | \([2]\) | \(53084160\) | \(3.1717\) | \(\Gamma_0(N)\)-optimal |
| 450840.by2 | 450840by2 | \([0, 1, 0, 9687184, -195311389680]\) | \(4067455675907516/669098843633025\) | \(-16538029574156648055014400\) | \([2]\) | \(106168320\) | \(3.5183\) |
Rank
sage: E.rank()
The elliptic curves in class 450840.by have rank \(0\).
Complex multiplication
The elliptic curves in class 450840.by do not have complex multiplication.Modular form 450840.2.a.by
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 LMFDB 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 LMFDB labels.
