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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 94640bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94640.n1 | 94640bi1 | \([0, 1, 0, -80500, -8158500]\) | \(46689225424/3901625\) | \(4821094058144000\) | \([2]\) | \(774144\) | \(1.7513\) | \(\Gamma_0(N)\)-optimal |
94640.n2 | 94640bi2 | \([0, 1, 0, 85120, -37241372]\) | \(13799183324/129390625\) | \(-639532885264000000\) | \([2]\) | \(1548288\) | \(2.0978\) |
Rank
sage: E.rank()
The elliptic curves in class 94640bi have rank \(1\).
Complex multiplication
The elliptic curves in class 94640bi do not have complex multiplication.Modular form 94640.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.