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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 496860dq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
496860.dq1 | 496860dq1 | \([0, 1, 0, -4681525, -3900229852]\) | \(1248870793216/42525\) | \(386378239088696400\) | \([2]\) | \(12441600\) | \(2.4663\) | \(\Gamma_0(N)\)-optimal |
496860.dq2 | 496860dq2 | \([0, 1, 0, -4474500, -4260618972]\) | \(-68150496976/14467005\) | \(-2103134031007592244480\) | \([2]\) | \(24883200\) | \(2.8129\) |
Rank
sage: E.rank()
The elliptic curves in class 496860dq have rank \(1\).
Complex multiplication
The elliptic curves in class 496860dq do not have complex multiplication.Modular form 496860.2.a.dq
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.