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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 6006b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6006.f2 | 6006b1 | \([1, 1, 0, -2258230, 680937556]\) | \(1273586744879073781899625/536167394157891944448\) | \(536167394157891944448\) | \([2]\) | \(267520\) | \(2.6745\) | \(\Gamma_0(N)\)-optimal |
6006.f1 | 6006b2 | \([1, 1, 0, -31094070, 66697709652]\) | \(3324730517043538694039691625/1498694078086994460672\) | \(1498694078086994460672\) | \([2]\) | \(535040\) | \(3.0210\) |
Rank
sage: E.rank()
The elliptic curves in class 6006b have rank \(1\).
Complex multiplication
The elliptic curves in class 6006b do not have complex multiplication.Modular form 6006.2.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 Cremona 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 Cremona labels.