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SageMath
E = EllipticCurve("ff1")
E.isogeny_class()
Elliptic curves in class 424830.ff
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.ff1 | 424830ff3 | \([1, 1, 1, -92627396, 343085724029]\) | \(30949975477232209/478125000\) | \(1357760658931228125000\) | \([2]\) | \(63700992\) | \(3.1901\) | \(\Gamma_0(N)\)-optimal* |
424830.ff2 | 424830ff2 | \([1, 1, 1, -5962076, 5021643773]\) | \(8253429989329/936360000\) | \(2659038474450917160000\) | \([2, 2]\) | \(31850496\) | \(2.8435\) | \(\Gamma_0(N)\)-optimal* |
424830.ff3 | 424830ff1 | \([1, 1, 1, -1430556, -575689731]\) | \(114013572049/15667200\) | \(44491101271858483200\) | \([2]\) | \(15925248\) | \(2.4969\) | \(\Gamma_0(N)\)-optimal* |
424830.ff4 | 424830ff4 | \([1, 1, 1, 8198924, 25277538173]\) | \(21464092074671/109596256200\) | \(-311227158242107598992200\) | \([2]\) | \(63700992\) | \(3.1901\) |
Rank
sage: E.rank()
The elliptic curves in class 424830.ff have rank \(1\).
Complex multiplication
The elliptic curves in class 424830.ff do not have complex multiplication.Modular form 424830.2.a.ff
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.