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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 106560fb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106560.bd2 | 106560fb1 | \([0, 0, 0, -13863, 630088]\) | \(-6315211203904/21390625\) | \(-998001000000\) | \([2]\) | \(184320\) | \(1.1665\) | \(\Gamma_0(N)\)-optimal |
106560.bd1 | 106560fb2 | \([0, 0, 0, -221988, 40257088]\) | \(405158291551936/4625\) | \(13810176000\) | \([2]\) | \(368640\) | \(1.5131\) |
Rank
sage: E.rank()
The elliptic curves in class 106560fb have rank \(0\).
Complex multiplication
The elliptic curves in class 106560fb do not have complex multiplication.Modular form 106560.2.a.fb
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.