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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 209814.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
209814.bi1 | 209814bs2 | \([1, 0, 1, -38749394412, -2092824878726870]\) | \(150476552140919246594353/42832838728685592576\) | \(1831582550111788095015225592848384\) | \([2]\) | \(1121402880\) | \(5.0892\) | |
209814.bi2 | 209814bs1 | \([1, 0, 1, -14399780332, 639279739814186]\) | \(7722211175253055152433/340131399900069888\) | \(14544418611807933368138666606592\) | \([2]\) | \(560701440\) | \(4.7426\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 209814.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 209814.bi do not have complex multiplication.Modular form 209814.2.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.