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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 890g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
890.g2 | 890g1 | \([1, 1, 1, 10, 147]\) | \(109902239/8900000\) | \(-8900000\) | \([5]\) | \(200\) | \(0.012969\) | \(\Gamma_0(N)\)-optimal |
890.g1 | 890g2 | \([1, 1, 1, -2040, -38093]\) | \(-938917686360961/55840594490\) | \(-55840594490\) | \([]\) | \(1000\) | \(0.81769\) |
Rank
sage: E.rank()
The elliptic curves in class 890g have rank \(1\).
Complex multiplication
The elliptic curves in class 890g do not have complex multiplication.Modular form 890.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.