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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 142.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142.b1 | 142c2 | \([1, -1, 0, -41, -91]\) | \(7727161833/40328\) | \(40328\) | \([2]\) | \(18\) | \(-0.27097\) | |
142.b2 | 142c1 | \([1, -1, 0, -1, -3]\) | \(-185193/4544\) | \(-4544\) | \([2]\) | \(9\) | \(-0.61754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 142.b have rank \(0\).
Complex multiplication
The elliptic curves in class 142.b do not have complex multiplication.Modular form 142.2.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.