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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 126960.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126960.n1 | 126960x2 | \([0, -1, 0, -41576, -353424]\) | \(159484621967/91125000\) | \(4541308416000000\) | \([2]\) | \(497664\) | \(1.6941\) | |
126960.n2 | 126960x1 | \([0, -1, 0, -26856, 1695600]\) | \(42985344527/216000\) | \(10764582912000\) | \([2]\) | \(248832\) | \(1.3475\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 126960.n have rank \(1\).
Complex multiplication
The elliptic curves in class 126960.n do not have complex multiplication.Modular form 126960.2.a.n
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.