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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 189618.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.bb1 | 189618p1 | \([1, 1, 1, -510468, -127896891]\) | \(3047678972871625/304559880768\) | \(1470052373529909312\) | \([2]\) | \(3612672\) | \(2.2224\) | \(\Gamma_0(N)\)-optimal |
189618.bb2 | 189618p2 | \([1, 1, 1, 631972, -617775163]\) | \(5783051584712375/37533175779528\) | \(-181165470651207766152\) | \([2]\) | \(7225344\) | \(2.5689\) |
Rank
sage: E.rank()
The elliptic curves in class 189618.bb have rank \(2\).
Complex multiplication
The elliptic curves in class 189618.bb do not have complex multiplication.Modular form 189618.2.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 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.