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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 321100.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
321100.g1 | 321100g1 | \([0, 1, 0, -3892633, 2755642488]\) | \(5405726654464/407253125\) | \(491433262257031250000\) | \([2]\) | \(11059200\) | \(2.7156\) | \(\Gamma_0(N)\)-optimal |
321100.g2 | 321100g2 | \([0, 1, 0, 3733492, 12242541988]\) | \(298091207216/3525390625\) | \(-68065548789062500000000\) | \([2]\) | \(22118400\) | \(3.0621\) |
Rank
sage: E.rank()
The elliptic curves in class 321100.g have rank \(1\).
Complex multiplication
The elliptic curves in class 321100.g do not have complex multiplication.Modular form 321100.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.