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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 443760v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.v2 | 443760v1 | \([0, -1, 0, -303414120, -2109353043600]\) | \(-119305480789133569/5200091136000\) | \(-134642335574191446687744000\) | \([2]\) | \(223534080\) | \(3.7792\) | \(\Gamma_0(N)\)-optimal* |
443760.v1 | 443760v2 | \([0, -1, 0, -4904317800, -132193463330448]\) | \(503835593418244309249/898614000000\) | \(23267186011808096256000000\) | \([2]\) | \(447068160\) | \(4.1257\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 443760v have rank \(0\).
Complex multiplication
The elliptic curves in class 443760v do not have complex multiplication.Modular form 443760.2.a.v
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.