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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 16731.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16731.b1 | 16731b2 | \([1, -1, 1, -25382, -1541510]\) | \(19034163/121\) | \(11495735867187\) | \([2]\) | \(55296\) | \(1.3431\) | |
16731.b2 | 16731b1 | \([1, -1, 1, -2567, 9910]\) | \(19683/11\) | \(1045066897017\) | \([2]\) | \(27648\) | \(0.99652\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16731.b have rank \(1\).
Complex multiplication
The elliptic curves in class 16731.b do not have complex multiplication.Modular form 16731.2.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.