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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 13650.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13650.q1 | 13650s1 | \([1, 1, 0, -2778575, -1589302875]\) | \(1214675547724509317/145065854029824\) | \(283331746152000000000\) | \([2]\) | \(506880\) | \(2.6554\) | \(\Gamma_0(N)\)-optimal |
13650.q2 | 13650s2 | \([1, 1, 0, 3981425, -8112702875]\) | \(3573626171578090363/16631459495816256\) | \(-32483319327766125000000\) | \([2]\) | \(1013760\) | \(3.0020\) |
Rank
sage: E.rank()
The elliptic curves in class 13650.q have rank \(1\).
Complex multiplication
The elliptic curves in class 13650.q do not have complex multiplication.Modular form 13650.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.