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SageMath
E = EllipticCurve("hg1")
E.isogeny_class()
Elliptic curves in class 310464hg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
310464.hg2 | 310464hg1 | \([0, 0, 0, -26460, -1333584]\) | \(54000/11\) | \(417342061559808\) | \([2]\) | \(1105920\) | \(1.5210\) | \(\Gamma_0(N)\)-optimal |
310464.hg1 | 310464hg2 | \([0, 0, 0, -132300, 17336592]\) | \(1687500/121\) | \(18363050708631552\) | \([2]\) | \(2211840\) | \(1.8676\) |
Rank
sage: E.rank()
The elliptic curves in class 310464hg have rank \(1\).
Complex multiplication
The elliptic curves in class 310464hg do not have complex multiplication.Modular form 310464.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.