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SageMath
E = EllipticCurve("hy1")
E.isogeny_class()
Elliptic curves in class 62400hy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
62400.fi2 | 62400hy1 | \([0, 1, 0, -993, 10143]\) | \(3307949/468\) | \(15335424000\) | \([2]\) | \(49152\) | \(0.68040\) | \(\Gamma_0(N)\)-optimal |
62400.fi1 | 62400hy2 | \([0, 1, 0, -4193, -95457]\) | \(248858189/27378\) | \(897122304000\) | \([2]\) | \(98304\) | \(1.0270\) |
Rank
sage: E.rank()
The elliptic curves in class 62400hy have rank \(1\).
Complex multiplication
The elliptic curves in class 62400hy do not have complex multiplication.Modular form 62400.2.a.hy
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.