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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 121275.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121275.bi1 | 121275fv2 | \([1, -1, 1, -8026430, 8750951822]\) | \(341385539669/160083\) | \(26815816304771484375\) | \([2]\) | \(3686400\) | \(2.6838\) | |
121275.bi2 | 121275fv1 | \([1, -1, 1, -584555, 88609322]\) | \(131872229/56133\) | \(9402948574400390625\) | \([2]\) | \(1843200\) | \(2.3373\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 121275.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 121275.bi do not have complex multiplication.Modular form 121275.2.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.