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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 22218.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22218.bi1 | 22218be2 | \([1, 0, 0, -14294, 3001002]\) | \(-2181825073/25039686\) | \(-3706772177290854\) | \([]\) | \(190080\) | \(1.6693\) | |
22218.bi2 | 22218be1 | \([1, 0, 0, 1576, -106344]\) | \(2924207/34776\) | \(-5148096075864\) | \([]\) | \(63360\) | \(1.1200\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22218.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 22218.bi do not have complex multiplication.Modular form 22218.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.