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SageMath
E = EllipticCurve("dq1")
E.isogeny_class()
Elliptic curves in class 176610dq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176610.a1 | 176610dq1 | \([1, 1, 0, -5904678, -5503982508]\) | \(1569388636061/6914880\) | \(100315173565617030720\) | \([2]\) | \(9354240\) | \(2.6904\) | \(\Gamma_0(N)\)-optimal |
176610.a2 | 176610dq2 | \([1, 1, 0, -2977998, -10958728692]\) | \(-201333092381/3458880600\) | \(-50178485777301352241400\) | \([2]\) | \(18708480\) | \(3.0370\) |
Rank
sage: E.rank()
The elliptic curves in class 176610dq have rank \(0\).
Complex multiplication
The elliptic curves in class 176610dq do not have complex multiplication.Modular form 176610.2.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.