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SageMath
E = EllipticCurve("cn1")
E.isogeny_class()
Elliptic curves in class 101136.cn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101136.cn1 | 101136cj2 | \([0, 1, 0, -46962400, -123902452108]\) | \(-23769846831649063249/3261823333284\) | \(-1571841037670520078336\) | \([]\) | \(10668672\) | \(3.0850\) | |
101136.cn2 | 101136cj1 | \([0, 1, 0, 124640, 37881332]\) | \(444369620591/1540767744\) | \(-742481036549554176\) | \([]\) | \(1524096\) | \(2.1121\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101136.cn have rank \(0\).
Complex multiplication
The elliptic curves in class 101136.cn do not have complex multiplication.Modular form 101136.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.