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SageMath
sage: E = EllipticCurve("g1")
sage: E.isogeny_class()
Elliptic curves in class 143745g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
143745.j3 | 143745g1 | [1, 0, 0, -3451, 73640] | [2] | 207360 | \(\Gamma_0(N)\)-optimal |
143745.j2 | 143745g2 | [1, 0, 0, -10296, -311049] | [2, 2] | 414720 | |
143745.j4 | 143745g3 | [1, 0, 0, 23929, -1933314] | [2] | 829440 | |
143745.j1 | 143745g4 | [1, 0, 0, -154041, -23281500] | [2] | 829440 |
Rank
sage: E.rank()
The elliptic curves in class 143745g have rank \(1\).
Complex multiplication
The elliptic curves in class 143745g do not have complex multiplication.Modular form 143745.2.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.