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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 43120cp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43120.cj1 | 43120cp1 | \([0, 1, 0, -800, 23540]\) | \(-117649/440\) | \(-212031733760\) | \([]\) | \(36288\) | \(0.85900\) | \(\Gamma_0(N)\)-optimal |
43120.cj2 | 43120cp2 | \([0, 1, 0, 7040, -562892]\) | \(80062991/332750\) | \(-160348998656000\) | \([]\) | \(108864\) | \(1.4083\) |
Rank
sage: E.rank()
The elliptic curves in class 43120cp have rank \(1\).
Complex multiplication
The elliptic curves in class 43120cp do not have complex multiplication.Modular form 43120.2.a.cp
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.