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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 12880.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12880.x1 | 12880w2 | \([0, -1, 0, -401920, 71442432]\) | \(1753007192038126081/478174101507200\) | \(1958601119773491200\) | \([2]\) | \(215040\) | \(2.2177\) | |
12880.x2 | 12880w1 | \([0, -1, 0, -145920, -20512768]\) | \(83890194895342081/3958384640000\) | \(16213543485440000\) | \([2]\) | \(107520\) | \(1.8711\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 12880.x have rank \(1\).
Complex multiplication
The elliptic curves in class 12880.x do not have complex multiplication.Modular form 12880.2.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.