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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 444360bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
444360.bs4 | 444360bs1 | \([0, 1, 0, -95396, -196992096]\) | \(-2533446736/440749575\) | \(-16703169321343276800\) | \([2]\) | \(10813440\) | \(2.3678\) | \(\Gamma_0(N)\)-optimal* |
444360.bs3 | 444360bs2 | \([0, 1, 0, -5692216, -5184878080]\) | \(134555337776164/1312250625\) | \(198922432371384960000\) | \([2, 2]\) | \(21626880\) | \(2.7144\) | \(\Gamma_0(N)\)-optimal* |
444360.bs2 | 444360bs3 | \([0, 1, 0, -10072336, 3887226464]\) | \(372749784765122/194143359375\) | \(58859898467378400000000\) | \([2]\) | \(43253760\) | \(3.0610\) | \(\Gamma_0(N)\)-optimal* |
444360.bs1 | 444360bs4 | \([0, 1, 0, -90861216, -333392136480]\) | \(273629163383866082/26408025\) | \(8006319017183692800\) | \([2]\) | \(43253760\) | \(3.0610\) |
Rank
sage: E.rank()
The elliptic curves in class 444360bs have rank \(1\).
Complex multiplication
The elliptic curves in class 444360bs do not have complex multiplication.Modular form 444360.2.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.