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SageMath
sage: E = EllipticCurve("z1")
sage: E.isogeny_class()
Elliptic curves in class 97020.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
97020.z1 | 97020bu4 | [0, 0, 0, -21871983, 20758643318] | [2] | 11943936 | |
97020.z2 | 97020bu2 | [0, 0, 0, -18855543, 31514220542] | [2] | 3981312 | |
97020.z3 | 97020bu1 | [0, 0, 0, -1173648, 496640333] | [2] | 1990656 | \(\Gamma_0(N)\)-optimal |
97020.z4 | 97020bu3 | [0, 0, 0, 4541712, 2379994337] | [2] | 5971968 |
Rank
sage: E.rank()
The elliptic curves in class 97020.z have rank \(1\).
Complex multiplication
The elliptic curves in class 97020.z do not have complex multiplication.Modular form 97020.2.a.z
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.