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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 360789.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
360789.c1 | 360789c1 | \([1, 1, 1, -89584, 9965240]\) | \(133667977897/4690257\) | \(2789874245083497\) | \([2]\) | \(1774080\) | \(1.7347\) | \(\Gamma_0(N)\)-optimal |
360789.c2 | 360789c2 | \([1, 1, 1, 32361, 35183466]\) | \(6300872423/901984941\) | \(-536521678097609061\) | \([2]\) | \(3548160\) | \(2.0813\) |
Rank
sage: E.rank()
The elliptic curves in class 360789.c have rank \(0\).
Complex multiplication
The elliptic curves in class 360789.c do not have complex multiplication.Modular form 360789.2.a.c
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.