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SageMath
E = EllipticCurve("go1")
E.isogeny_class()
Elliptic curves in class 100800go
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.fj1 | 100800go1 | \([0, 0, 0, -25500, -1150000]\) | \(78608/21\) | \(489888000000000\) | \([2]\) | \(327680\) | \(1.5271\) | \(\Gamma_0(N)\)-optimal |
100800.fj2 | 100800go2 | \([0, 0, 0, 64500, -7450000]\) | \(318028/441\) | \(-41150592000000000\) | \([2]\) | \(655360\) | \(1.8737\) |
Rank
sage: E.rank()
The elliptic curves in class 100800go have rank \(1\).
Complex multiplication
The elliptic curves in class 100800go do not have complex multiplication.Modular form 100800.2.a.go
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 Cremona 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 Cremona labels.