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SageMath
E = EllipticCurve("hq1")
E.isogeny_class()
Elliptic curves in class 388080hq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.hq1 | 388080hq1 | \([0, 0, 0, -2352, 40131]\) | \(28311552/2695\) | \(136971671760\) | \([2]\) | \(516096\) | \(0.87479\) | \(\Gamma_0(N)\)-optimal |
388080.hq2 | 388080hq2 | \([0, 0, 0, 2793, 191394]\) | \(2963088/21175\) | \(-17219295878400\) | \([2]\) | \(1032192\) | \(1.2214\) |
Rank
sage: E.rank()
The elliptic curves in class 388080hq have rank \(0\).
Complex multiplication
The elliptic curves in class 388080hq do not have complex multiplication.Modular form 388080.2.a.hq
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.