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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 409101.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.v1 | 409101v2 | \([0, -1, 1, -4173297, -3279928345]\) | \(564661380021747712/27978783021\) | \(398292777080153109\) | \([]\) | \(8957952\) | \(2.4486\) | |
409101.v2 | 409101v1 | \([0, -1, 1, -98457, 4902050]\) | \(7414712369152/3571421301\) | \(50841071501603229\) | \([]\) | \(2985984\) | \(1.8993\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 409101.v have rank \(1\).
Complex multiplication
The elliptic curves in class 409101.v do not have complex multiplication.Modular form 409101.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.