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SageMath
E = EllipticCurve("nu1")
E.isogeny_class()
Elliptic curves in class 446400.nu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
446400.nu1 | 446400nu2 | \([0, 0, 0, -28980300, 21040198000]\) | \(901456690969801/457629750000\) | \(1366475111424000000000000\) | \([2]\) | \(70778880\) | \(3.3237\) | \(\Gamma_0(N)\)-optimal* |
446400.nu2 | 446400nu1 | \([0, 0, 0, 6731700, 2541382000]\) | \(11298232190519/7472736000\) | \(-22313470132224000000000\) | \([2]\) | \(35389440\) | \(2.9771\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 446400.nu have rank \(2\).
Complex multiplication
The elliptic curves in class 446400.nu do not have complex multiplication.Modular form 446400.2.a.nu
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.