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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1800g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1800.v3 | 1800g1 | \([0, 0, 0, -450, -3375]\) | \(55296/5\) | \(911250000\) | \([2]\) | \(768\) | \(0.45866\) | \(\Gamma_0(N)\)-optimal |
1800.v2 | 1800g2 | \([0, 0, 0, -1575, 20250]\) | \(148176/25\) | \(72900000000\) | \([2, 2]\) | \(1536\) | \(0.80524\) | |
1800.v1 | 1800g3 | \([0, 0, 0, -24075, 1437750]\) | \(132304644/5\) | \(58320000000\) | \([2]\) | \(3072\) | \(1.1518\) | |
1800.v4 | 1800g4 | \([0, 0, 0, 2925, 114750]\) | \(237276/625\) | \(-7290000000000\) | \([2]\) | \(3072\) | \(1.1518\) |
Rank
sage: E.rank()
The elliptic curves in class 1800g have rank \(0\).
Complex multiplication
The elliptic curves in class 1800g do not have complex multiplication.Modular form 1800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.