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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 119952.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
119952.bi1 | 119952gu2 | \([0, 0, 0, -1961211, 1046700074]\) | \(814544990575471/9268826496\) | \(9493062692230397952\) | \([2]\) | \(3096576\) | \(2.4547\) | |
119952.bi2 | 119952gu1 | \([0, 0, 0, -25851, 41474090]\) | \(-1865409391/724451328\) | \(-741977625446055936\) | \([2]\) | \(1548288\) | \(2.1082\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 119952.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 119952.bi do not have complex multiplication.Modular form 119952.2.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.