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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 38808.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38808.n1 | 38808g2 | \([0, 0, 0, -40131, 2991646]\) | \(3203226/121\) | \(269998559373312\) | \([2]\) | \(129024\) | \(1.5375\) | |
38808.n2 | 38808g1 | \([0, 0, 0, 1029, 168070]\) | \(108/11\) | \(-12272661789696\) | \([2]\) | \(64512\) | \(1.1910\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38808.n have rank \(0\).
Complex multiplication
The elliptic curves in class 38808.n do not have complex multiplication.Modular form 38808.2.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 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.