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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 299832.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
299832.r1 | 299832r1 | \([0, 1, 0, -625931, -179280138]\) | \(1909913257984/129730653\) | \(1842182913216539088\) | \([2]\) | \(7257600\) | \(2.2534\) | \(\Gamma_0(N)\)-optimal |
299832.r2 | 299832r2 | \([0, 1, 0, 541684, -770093328]\) | \(77366117936/1172914587\) | \(-266487299446040255232\) | \([2]\) | \(14515200\) | \(2.6000\) |
Rank
sage: E.rank()
The elliptic curves in class 299832.r have rank \(1\).
Complex multiplication
The elliptic curves in class 299832.r do not have complex multiplication.Modular form 299832.2.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 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.