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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 327990.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
327990.bi1 | 327990bi1 | \([1, 0, 0, -419256, 104243760]\) | \(13701674594089/31758480\) | \(18890684543512080\) | \([2]\) | \(4730880\) | \(2.0038\) | \(\Gamma_0(N)\)-optimal |
327990.bi2 | 327990bi2 | \([1, 0, 0, -267876, 180569556]\) | \(-3573857582569/21617820900\) | \(-12858784020521208900\) | \([2]\) | \(9461760\) | \(2.3504\) |
Rank
sage: E.rank()
The elliptic curves in class 327990.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 327990.bi do not have complex multiplication.Modular form 327990.2.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.