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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 151008g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
151008.bq2 | 151008g1 | \([0, 1, 0, -11898, -223236]\) | \(1643032000/767637\) | \(87034609366848\) | \([2]\) | \(409600\) | \(1.3692\) | \(\Gamma_0(N)\)-optimal |
151008.bq1 | 151008g2 | \([0, 1, 0, -158913, -24421905]\) | \(61162984000/41067\) | \(297995041124352\) | \([2]\) | \(819200\) | \(1.7158\) |
Rank
sage: E.rank()
The elliptic curves in class 151008g have rank \(0\).
Complex multiplication
The elliptic curves in class 151008g do not have complex multiplication.Modular form 151008.2.a.g
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.