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SageMath
E = EllipticCurve("gb1")
E.isogeny_class()
Elliptic curves in class 278850.gb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
278850.gb1 | 278850gb1 | \([1, 1, 1, -24396844313, 1468273599205031]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-1976817279494940463463454000000\) | \([]\) | \(829785600\) | \(4.7230\) | \(\Gamma_0(N)\)-optimal |
278850.gb2 | 278850gb2 | \([1, 1, 1, 69091800937, -92148845193492469]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-3689399873710522176230009556361968750\) | \([]\) | \(5808499200\) | \(5.6960\) |
Rank
sage: E.rank()
The elliptic curves in class 278850.gb have rank \(0\).
Complex multiplication
The elliptic curves in class 278850.gb do not have complex multiplication.Modular form 278850.2.a.gb
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.