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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 116610.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116610.bi1 | 116610bi2 | \([1, 0, 1, -132838, -12917344]\) | \(53706380371489/16171875000\) | \(78058551796875000\) | \([2]\) | \(1128960\) | \(1.9466\) | |
116610.bi2 | 116610bi1 | \([1, 0, 1, 22642, -1349632]\) | \(265971760991/317400000\) | \(-1532029176600000\) | \([2]\) | \(564480\) | \(1.6000\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116610.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 116610.bi do not have complex multiplication.Modular form 116610.2.a.bi
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.