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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1800.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1800.g1 | 1800j2 | \([0, 0, 0, -37875, 1768750]\) | \(2060602/729\) | \(2125764000000000\) | \([2]\) | \(7680\) | \(1.6422\) | |
1800.g2 | 1800j1 | \([0, 0, 0, 7125, 193750]\) | \(27436/27\) | \(-39366000000000\) | \([2]\) | \(3840\) | \(1.2957\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1800.g have rank \(1\).
Complex multiplication
The elliptic curves in class 1800.g 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 LMFDB 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 LMFDB labels.