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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 8372.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8372.g1 | 8372e1 | \([0, 1, 0, -189, 2303]\) | \(-2932006912/7750379\) | \(-1984097024\) | \([3]\) | \(3456\) | \(0.47158\) | \(\Gamma_0(N)\)-optimal |
8372.g2 | 8372e2 | \([0, 1, 0, 1651, -52897]\) | \(1942951190528/5944921619\) | \(-1521899934464\) | \([]\) | \(10368\) | \(1.0209\) |
Rank
sage: E.rank()
The elliptic curves in class 8372.g have rank \(1\).
Complex multiplication
The elliptic curves in class 8372.g do not have complex multiplication.Modular form 8372.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.