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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 405042.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
405042.br1 | 405042br2 | \([1, 0, 1, -400026635, -2195203556554]\) | \(150476552140919246594353/42832838728685592576\) | \(2015108633721933674744979456\) | \([2]\) | \(231289344\) | \(3.9459\) | |
405042.br2 | 405042br1 | \([1, 0, 1, -148655115, 670532320054]\) | \(7722211175253055152433/340131399900069888\) | \(16001781364062099842531328\) | \([2]\) | \(115644672\) | \(3.5993\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 405042.br have rank \(1\).
Complex multiplication
The elliptic curves in class 405042.br do not have complex multiplication.Modular form 405042.2.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.