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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 6930.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6930.g1 | 6930j1 | \([1, -1, 0, -44955, 3679825]\) | \(13782741913468081/701662500\) | \(511511962500\) | \([2]\) | \(23040\) | \(1.3167\) | \(\Gamma_0(N)\)-optimal |
6930.g2 | 6930j2 | \([1, -1, 0, -42525, 4093411]\) | \(-11666347147400401/3126621093750\) | \(-2279306777343750\) | \([2]\) | \(46080\) | \(1.6633\) |
Rank
sage: E.rank()
The elliptic curves in class 6930.g have rank \(0\).
Complex multiplication
The elliptic curves in class 6930.g do not have complex multiplication.Modular form 6930.2.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.