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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 56550.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56550.g1 | 56550i4 | \([1, 1, 0, -104414875, -410712246875]\) | \(8057323694463985606146481/638717154543000\) | \(9979955539734375000\) | \([2]\) | \(6635520\) | \(3.0915\) | |
56550.g2 | 56550i2 | \([1, 1, 0, -6539875, -6390621875]\) | \(1979758117698975186481/17510434929000000\) | \(273600545765625000000\) | \([2, 2]\) | \(3317760\) | \(2.7449\) | |
56550.g3 | 56550i3 | \([1, 1, 0, -1976875, -15137892875]\) | \(-54681655838565466801/6303365630859375000\) | \(-98490087982177734375000\) | \([2]\) | \(6635520\) | \(3.0915\) | |
56550.g4 | 56550i1 | \([1, 1, 0, -707875, 65402125]\) | \(2510581756496128561/1333551278592000\) | \(20836738728000000000\) | \([2]\) | \(1658880\) | \(2.3984\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 56550.g have rank \(1\).
Complex multiplication
The elliptic curves in class 56550.g do not have complex multiplication.Modular form 56550.2.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.