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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 493680n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
493680.n2 | 493680n1 | \([0, -1, 0, 27064, 1148160]\) | \(907924/765\) | \(-1847121903221760\) | \([2]\) | \(2297856\) | \(1.6170\) | \(\Gamma_0(N)\)-optimal* |
493680.n1 | 493680n2 | \([0, -1, 0, -132656, 10220256]\) | \(53461798/21675\) | \(104670241182566400\) | \([2]\) | \(4595712\) | \(1.9636\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 493680n have rank \(0\).
Complex multiplication
The elliptic curves in class 493680n do not have complex multiplication.Modular form 493680.2.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 Cremona 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 Cremona labels.