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SageMath
E = EllipticCurve("ga1")
E.isogeny_class()
Elliptic curves in class 364650.ga
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
364650.ga1 | 364650ga1 | \([1, 0, 0, -68638, -6922108]\) | \(18309982521293/15402816\) | \(30083625000000\) | \([2]\) | \(1628160\) | \(1.5139\) | \(\Gamma_0(N)\)-optimal |
364650.ga2 | 364650ga2 | \([1, 0, 0, -53638, -10027108]\) | \(-8737997316173/17161945944\) | \(-33519425671875000\) | \([2]\) | \(3256320\) | \(1.8604\) |
Rank
sage: E.rank()
The elliptic curves in class 364650.ga have rank \(1\).
Complex multiplication
The elliptic curves in class 364650.ga do not have complex multiplication.Modular form 364650.2.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.