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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 1710r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1710.s2 | 1710r1 | \([1, -1, 1, -887, -10929]\) | \(-105756712489/12476160\) | \(-9095120640\) | \([2]\) | \(1536\) | \(0.64672\) | \(\Gamma_0(N)\)-optimal |
1710.s1 | 1710r2 | \([1, -1, 1, -14567, -673041]\) | \(468898230633769/5540400\) | \(4038951600\) | \([2]\) | \(3072\) | \(0.99330\) |
Rank
sage: E.rank()
The elliptic curves in class 1710r have rank \(0\).
Complex multiplication
The elliptic curves in class 1710r do not have complex multiplication.Modular form 1710.2.a.r
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.