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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 105966.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
105966.bd1 | 105966j2 | \([1, -1, 0, -1522788, 151363088]\) | \(39661299/21952\) | \(216147078411827040576\) | \([]\) | \(4510080\) | \(2.5924\) | |
105966.bd2 | 105966j1 | \([1, -1, 0, -1156953, 479273193]\) | \(12680118891/28\) | \(378186288198516\) | \([3]\) | \(1503360\) | \(2.0430\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 105966.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 105966.bd do not have complex multiplication.Modular form 105966.2.a.bd
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.