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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 193200bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
193200.gg1 | 193200bb1 | \([0, 1, 0, -8533, -941437]\) | \(-1073741824/5325075\) | \(-340804800000000\) | \([]\) | \(746496\) | \(1.4730\) | \(\Gamma_0(N)\)-optimal |
193200.gg2 | 193200bb2 | \([0, 1, 0, 75467, 22998563]\) | \(742692847616/3992296875\) | \(-255507000000000000\) | \([]\) | \(2239488\) | \(2.0223\) |
Rank
sage: E.rank()
The elliptic curves in class 193200bb have rank \(0\).
Complex multiplication
The elliptic curves in class 193200bb do not have complex multiplication.Modular form 193200.2.a.bb
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.