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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 10890bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10890.bv4 | 10890bi1 | \([1, -1, 1, 703, -2131]\) | \(804357/500\) | \(-23916073500\) | \([2]\) | \(8640\) | \(0.68059\) | \(\Gamma_0(N)\)-optimal |
10890.bv3 | 10890bi2 | \([1, -1, 1, -2927, -15199]\) | \(57960603/31250\) | \(1494754593750\) | \([2]\) | \(17280\) | \(1.0272\) | |
10890.bv2 | 10890bi3 | \([1, -1, 1, -8372, 337879]\) | \(-1860867/320\) | \(-11158283252160\) | \([2]\) | \(25920\) | \(1.2299\) | |
10890.bv1 | 10890bi4 | \([1, -1, 1, -139052, 19992151]\) | \(8527173507/200\) | \(6973927032600\) | \([2]\) | \(51840\) | \(1.5765\) |
Rank
sage: E.rank()
The elliptic curves in class 10890bi have rank \(0\).
Complex multiplication
The elliptic curves in class 10890bi do not have complex multiplication.Modular form 10890.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.