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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 236992.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
236992.r1 | 236992r2 | \([0, 1, 0, -1033313, -404606081]\) | \(12576878500/1127\) | \(10933793384235008\) | \([2]\) | \(2703360\) | \(2.1176\) | |
236992.r2 | 236992r1 | \([0, 1, 0, -59953, -7280529]\) | \(-9826000/3703\) | \(-8981330279907328\) | \([2]\) | \(1351680\) | \(1.7710\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 236992.r have rank \(1\).
Complex multiplication
The elliptic curves in class 236992.r do not have complex multiplication.Modular form 236992.2.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.