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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 25200.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25200.br1 | 25200dd2 | \([0, 0, 0, -73672875, 243393356250]\) | \(280844088456303/614656\) | \(96786192384000000000\) | \([2]\) | \(2211840\) | \(3.0813\) | |
25200.br2 | 25200dd1 | \([0, 0, 0, -4552875, 3892556250]\) | \(-66282611823/3211264\) | \(-505658474496000000000\) | \([2]\) | \(1105920\) | \(2.7347\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25200.br have rank \(1\).
Complex multiplication
The elliptic curves in class 25200.br do not have complex multiplication.Modular form 25200.2.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.