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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 54150.cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54150.cq1 | 54150cj2 | \([1, 0, 0, -232673713, -1365897858583]\) | \(276288773643091/41990400\) | \(211715398512801900000000\) | \([2]\) | \(9338880\) | \(3.4883\) | |
54150.cq2 | 54150cj1 | \([1, 0, 0, -13185713, -25484642583]\) | \(-50284268371/26542080\) | \(-133825042022906880000000\) | \([2]\) | \(4669440\) | \(3.1418\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54150.cq have rank \(1\).
Complex multiplication
The elliptic curves in class 54150.cq do not have complex multiplication.Modular form 54150.2.a.cq
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.