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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 274890bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
274890.bs4 | 274890bs1 | \([1, 0, 1, -173829, 4561456]\) | \(4937402992298041/2780405760000\) | \(327111957258240000\) | \([2]\) | \(3538944\) | \(2.0508\) | \(\Gamma_0(N)\)-optimal |
274890.bs2 | 274890bs2 | \([1, 0, 1, -1741829, -880417744]\) | \(4967657717692586041/29490113030400\) | \(3469482307913529600\) | \([2, 2]\) | \(7077888\) | \(2.3974\) | |
274890.bs3 | 274890bs3 | \([1, 0, 1, -742229, -1883616304]\) | \(-384369029857072441/12804787777021680\) | \(-1506470477178823630320\) | \([2]\) | \(14155776\) | \(2.7440\) | |
274890.bs1 | 274890bs4 | \([1, 0, 1, -27829429, -56509615984]\) | \(20260414982443110947641/720358602480\) | \(84749469223169520\) | \([2]\) | \(14155776\) | \(2.7440\) |
Rank
sage: E.rank()
The elliptic curves in class 274890bs have rank \(0\).
Complex multiplication
The elliptic curves in class 274890bs do not have complex multiplication.Modular form 274890.2.a.bs
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 Cremona 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 Cremona labels.