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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 45675.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
45675.bg1 | 45675p2 | \([1, -1, 0, -34767, -2486484]\) | \(408023180713/1421\) | \(16186078125\) | \([2]\) | \(73728\) | \(1.1784\) | |
45675.bg2 | 45675p1 | \([1, -1, 0, -2142, -39609]\) | \(-95443993/5887\) | \(-67056609375\) | \([2]\) | \(36864\) | \(0.83182\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 45675.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 45675.bg do not have complex multiplication.Modular form 45675.2.a.bg
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.