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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 1650.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1650.g1 | 1650j2 | \([1, 0, 1, -3051, -133802]\) | \(-5023028944825/9420668928\) | \(-5887918080000\) | \([]\) | \(3888\) | \(1.1402\) | |
1650.g2 | 1650j1 | \([1, 0, 1, 324, 3898]\) | \(6045109175/13856832\) | \(-8660520000\) | \([3]\) | \(1296\) | \(0.59090\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1650.g have rank \(1\).
Complex multiplication
The elliptic curves in class 1650.g do not have complex multiplication.Modular form 1650.2.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 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.