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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 84525.cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84525.cn1 | 84525r4 | \([1, 1, 0, -6187500, -5926564125]\) | \(14251520160844849/264449745\) | \(486128875773515625\) | \([2]\) | \(2211840\) | \(2.5187\) | |
84525.cn2 | 84525r2 | \([1, 1, 0, -399375, -86346000]\) | \(3832302404449/472410225\) | \(868415477516015625\) | \([2, 2]\) | \(1105920\) | \(2.1721\) | |
84525.cn3 | 84525r1 | \([1, 1, 0, -99250, 10594375]\) | \(58818484369/7455105\) | \(13704463252265625\) | \([2]\) | \(552960\) | \(1.8256\) | \(\Gamma_0(N)\)-optimal |
84525.cn4 | 84525r3 | \([1, 1, 0, 586750, -444309375]\) | \(12152722588271/53476250625\) | \(-98303553277822265625\) | \([2]\) | \(2211840\) | \(2.5187\) |
Rank
sage: E.rank()
The elliptic curves in class 84525.cn have rank \(1\).
Complex multiplication
The elliptic curves in class 84525.cn do not have complex multiplication.Modular form 84525.2.a.cn
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.