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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 38829.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38829.b1 | 38829h2 | \([1, 0, 0, -389253, -90721674]\) | \(12977875/441\) | \(221643341864147763\) | \([2]\) | \(544896\) | \(2.1005\) | |
38829.b2 | 38829h1 | \([1, 0, 0, 8282, -4933621]\) | \(125/21\) | \(-10554444850673703\) | \([2]\) | \(272448\) | \(1.7539\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38829.b have rank \(0\).
Complex multiplication
The elliptic curves in class 38829.b do not have complex multiplication.Modular form 38829.2.a.b
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.