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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 116160.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116160.x1 | 116160ff4 | \([0, -1, 0, -174401, 27018081]\) | \(5052857764/219615\) | \(25497525879767040\) | \([2]\) | \(983040\) | \(1.9116\) | |
116160.x2 | 116160ff2 | \([0, -1, 0, -29201, -1353999]\) | \(94875856/27225\) | \(790212578918400\) | \([2, 2]\) | \(491520\) | \(1.5651\) | |
116160.x3 | 116160ff1 | \([0, -1, 0, -26781, -1677795]\) | \(1171019776/165\) | \(299322946560\) | \([2]\) | \(245760\) | \(1.2185\) | \(\Gamma_0(N)\)-optimal |
116160.x4 | 116160ff3 | \([0, -1, 0, 77279, -9041855]\) | \(439608956/556875\) | \(-64653756456960000\) | \([2]\) | \(983040\) | \(1.9116\) |
Rank
sage: E.rank()
The elliptic curves in class 116160.x have rank \(1\).
Complex multiplication
The elliptic curves in class 116160.x do not have complex multiplication.Modular form 116160.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.