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SageMath
E = EllipticCurve("nq1")
E.isogeny_class()
Elliptic curves in class 486720.nq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
486720.nq1 | 486720nq1 | \([0, 0, 0, -28392, 1849874]\) | \(-303464448/1625\) | \(-13553679672000\) | \([]\) | \(1161216\) | \(1.3643\) | \(\Gamma_0(N)\)-optimal |
486720.nq2 | 486720nq2 | \([0, 0, 0, 73008, 9846954]\) | \(7077888/10985\) | \(-66793075570802880\) | \([]\) | \(3483648\) | \(1.9136\) |
Rank
sage: E.rank()
The elliptic curves in class 486720.nq have rank \(2\).
Complex multiplication
The elliptic curves in class 486720.nq do not have complex multiplication.Modular form 486720.2.a.nq
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.