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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 528.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
528.g1 | 528h3 | \([0, 1, 0, -2344, -44428]\) | \(347873904937/395307\) | \(1619177472\) | \([2]\) | \(384\) | \(0.68052\) | |
528.g2 | 528h2 | \([0, 1, 0, -184, -364]\) | \(169112377/88209\) | \(361304064\) | \([2, 2]\) | \(192\) | \(0.33394\) | |
528.g3 | 528h1 | \([0, 1, 0, -104, 372]\) | \(30664297/297\) | \(1216512\) | \([2]\) | \(96\) | \(-0.012632\) | \(\Gamma_0(N)\)-optimal |
528.g4 | 528h4 | \([0, 1, 0, 696, -2124]\) | \(9090072503/5845851\) | \(-23944605696\) | \([4]\) | \(384\) | \(0.68052\) |
Rank
sage: E.rank()
The elliptic curves in class 528.g have rank \(1\).
Complex multiplication
The elliptic curves in class 528.g do not have complex multiplication.Modular form 528.2.a.g
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.