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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 333795.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
333795.x1 | 333795x2 | \([1, 0, 0, -5115306, -4449063339]\) | \(613260573399028801/699742803375\) | \(16890090198717495375\) | \([2]\) | \(9289728\) | \(2.6027\) | |
333795.x2 | 333795x1 | \([1, 0, 0, -238431, -105718464]\) | \(-62103840598801/164013609375\) | \(-3958889813228109375\) | \([2]\) | \(4644864\) | \(2.2561\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 333795.x have rank \(1\).
Complex multiplication
The elliptic curves in class 333795.x do not have complex multiplication.Modular form 333795.2.a.x
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.