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SageMath
E = EllipticCurve("hg1")
E.isogeny_class()
Elliptic curves in class 198450hg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
198450.cd2 | 198450hg1 | \([1, -1, 0, 5283, -16059]\) | \(109503/64\) | \(-9529569000000\) | \([]\) | \(373248\) | \(1.1799\) | \(\Gamma_0(N)\)-optimal |
198450.cd1 | 198450hg2 | \([1, -1, 0, -68217, 7505441]\) | \(-35937/4\) | \(-3907718888062500\) | \([]\) | \(1119744\) | \(1.7292\) |
Rank
sage: E.rank()
The elliptic curves in class 198450hg have rank \(0\).
Complex multiplication
The elliptic curves in class 198450hg do not have complex multiplication.Modular form 198450.2.a.hg
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.