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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 6864.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6864.g1 | 6864j1 | \([0, -1, 0, -92390416, -342145483328]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-107360947764024156094464\) | \([]\) | \(846720\) | \(3.3290\) | \(\Gamma_0(N)\)-optimal |
6864.g2 | 6864j2 | \([0, -1, 0, 261649424, 21474752782912]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-200371309594800856086420578304\) | \([]\) | \(5927040\) | \(4.3019\) |
Rank
sage: E.rank()
The elliptic curves in class 6864.g have rank \(0\).
Complex multiplication
The elliptic curves in class 6864.g do not have complex multiplication.Modular form 6864.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.