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SageMath
E = EllipticCurve("nd1")
E.isogeny_class()
Elliptic curves in class 262080nd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262080.nd2 | 262080nd1 | \([0, 0, 0, -18624492, 54028314576]\) | \(-553867390580563692/657061767578125\) | \(-847573599600000000000000\) | \([2]\) | \(31997952\) | \(3.2853\) | \(\Gamma_0(N)\)-optimal |
262080.nd1 | 262080nd2 | \([0, 0, 0, -356124492, 2585683314576]\) | \(1936101054887046531846/905403781953125\) | \(2335842322374113280000000\) | \([2]\) | \(63995904\) | \(3.6319\) |
Rank
sage: E.rank()
The elliptic curves in class 262080nd have rank \(1\).
Complex multiplication
The elliptic curves in class 262080nd do not have complex multiplication.Modular form 262080.2.a.nd
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.