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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 111600.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111600.br1 | 111600fe2 | \([0, 0, 0, -7245075, -2630024750]\) | \(901456690969801/457629750000\) | \(21351173616000000000000\) | \([2]\) | \(8847360\) | \(2.9771\) | |
111600.br2 | 111600fe1 | \([0, 0, 0, 1682925, -317672750]\) | \(11298232190519/7472736000\) | \(-348647970816000000000\) | \([2]\) | \(4423680\) | \(2.6305\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 111600.br have rank \(0\).
Complex multiplication
The elliptic curves in class 111600.br do not have complex multiplication.Modular form 111600.2.a.br
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.