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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 193600.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193600.bi1 | 193600gh2 | \([0, 1, 0, -35713, 2585823]\) | \(6352571665/2\) | \(1585971200\) | \([]\) | \(331776\) | \(1.1269\) | |
193600.bi2 | 193600gh1 | \([0, 1, 0, -513, 2143]\) | \(18865/8\) | \(6343884800\) | \([]\) | \(110592\) | \(0.57761\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 193600.bi have rank \(2\).
Complex multiplication
The elliptic curves in class 193600.bi do not have complex multiplication.Modular form 193600.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.