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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 266805bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
266805.bl2 | 266805bl1 | \([1, -1, 1, -3291707, 2209172914]\) | \(2803221/125\) | \(175889444200135367625\) | \([2]\) | \(11289600\) | \(2.6474\) | \(\Gamma_0(N)\)-optimal |
266805.bl1 | 266805bl2 | \([1, -1, 1, -8894612, -7302318614]\) | \(55306341/15625\) | \(21986180525016920953125\) | \([2]\) | \(22579200\) | \(2.9939\) |
Rank
sage: E.rank()
The elliptic curves in class 266805bl have rank \(0\).
Complex multiplication
The elliptic curves in class 266805bl do not have complex multiplication.Modular form 266805.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.