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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 317900bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
317900.bi1 | 317900bi1 | \([0, -1, 0, -3188633, -2122012738]\) | \(594160697344/21156245\) | \(127665080867101250000\) | \([2]\) | \(9953280\) | \(2.6285\) | \(\Gamma_0(N)\)-optimal |
317900.bi2 | 317900bi2 | \([0, -1, 0, 1182492, -7498496488]\) | \(1893932336/252651025\) | \(-24393526195432900000000\) | \([2]\) | \(19906560\) | \(2.9751\) |
Rank
sage: E.rank()
The elliptic curves in class 317900bi have rank \(1\).
Complex multiplication
The elliptic curves in class 317900bi do not have complex multiplication.Modular form 317900.2.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.