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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 22050.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22050.g1 | 22050bw1 | \([1, -1, 0, -240417, 25935741]\) | \(393349474783/153600000\) | \(600112800000000000\) | \([2]\) | \(430080\) | \(2.1100\) | \(\Gamma_0(N)\)-optimal |
22050.g2 | 22050bw2 | \([1, -1, 0, 767583, 186207741]\) | \(12801408679457/11250000000\) | \(-43953574218750000000\) | \([2]\) | \(860160\) | \(2.4566\) |
Rank
sage: E.rank()
The elliptic curves in class 22050.g have rank \(1\).
Complex multiplication
The elliptic curves in class 22050.g do not have complex multiplication.Modular form 22050.2.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.