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SageMath
E = EllipticCurve("gg1")
E.isogeny_class()
Elliptic curves in class 346800.gg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
346800.gg1 | 346800gg2 | \([0, 1, 0, -15042336808, 710097542878388]\) | \(-843137281012581793/216\) | \(-96432870864384000000\) | \([]\) | \(299811456\) | \(4.1170\) | |
346800.gg2 | 346800gg1 | \([0, 1, 0, -185424808, 977133118388]\) | \(-1579268174113/10077696\) | \(-4499172023048699904000000\) | \([]\) | \(99937152\) | \(3.5677\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 346800.gg have rank \(0\).
Complex multiplication
The elliptic curves in class 346800.gg do not have complex multiplication.Modular form 346800.2.a.gg
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.