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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 22080cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22080.bu2 | 22080cp1 | \([0, 1, 0, -128161, -18458785]\) | \(-3552342505518244/179863605135\) | \(-11787541226127360\) | \([2]\) | \(168960\) | \(1.8444\) | \(\Gamma_0(N)\)-optimal |
| 22080.bu1 | 22080cp2 | \([0, 1, 0, -2074881, -1151060481]\) | \(7536914291382802562/17961229575\) | \(2354214282854400\) | \([2]\) | \(337920\) | \(2.1910\) |
Rank
sage: E.rank()
The elliptic curves in class 22080cp have rank \(0\).
Complex multiplication
The elliptic curves in class 22080cp do not have complex multiplication.Modular form 22080.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
