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SageMath
sage: E = EllipticCurve("g1")
sage: E.isogeny_class()
Elliptic curves in class 55545g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
55545.t3 | 55545g1 | [1, 0, 1, -1334, -17869] | [2] | 45056 | \(\Gamma_0(N)\)-optimal |
55545.t2 | 55545g2 | [1, 0, 1, -3979, 74177] | [2, 2] | 90112 | |
55545.t4 | 55545g3 | [1, 0, 1, 9246, 465637] | [2] | 180224 | |
55545.t1 | 55545g4 | [1, 0, 1, -59524, 5584241] | [2] | 180224 |
Rank
sage: E.rank()
The elliptic curves in class 55545g have rank \(1\).
Complex multiplication
The elliptic curves in class 55545g do not have complex multiplication.Modular form 55545.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.