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SageMath
E = EllipticCurve("ga1")
E.isogeny_class()
Elliptic curves in class 81600.ga
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81600.ga1 | 81600iw1 | \([0, 1, 0, -4033, -63937]\) | \(1771561/612\) | \(2506752000000\) | \([2]\) | \(122880\) | \(1.0809\) | \(\Gamma_0(N)\)-optimal |
81600.ga2 | 81600iw2 | \([0, 1, 0, 11967, -431937]\) | \(46268279/46818\) | \(-191766528000000\) | \([2]\) | \(245760\) | \(1.4275\) |
Rank
sage: E.rank()
The elliptic curves in class 81600.ga have rank \(0\).
Complex multiplication
The elliptic curves in class 81600.ga do not have complex multiplication.Modular form 81600.2.a.ga
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.