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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 481338n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
481338.n2 | 481338n1 | \([1, -1, 0, -448443, 122476261]\) | \(-10278752783033483/717973880832\) | \(-696649338597408768\) | \([2]\) | \(9787392\) | \(2.1744\) | \(\Gamma_0(N)\)-optimal* |
481338.n1 | 481338n2 | \([1, -1, 0, -7291323, 7579846885]\) | \(44181166128077784203/195126437376\) | \(189330987059495424\) | \([2]\) | \(19574784\) | \(2.5210\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 481338n have rank \(1\).
Complex multiplication
The elliptic curves in class 481338n do not have complex multiplication.Modular form 481338.2.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.