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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 244881.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244881.bk1 | 244881bk3 | \([0, 0, 1, -22555911846, 1303883396055828]\) | \(-360675992659311050823073792/56219378022244619\) | \(-197821585663073772322072059\) | \([]\) | \(352719360\) | \(4.4501\) | |
| 244881.bk2 | 244881bk2 | \([0, 0, 1, -242674536, 2265147188073]\) | \(-449167881463536812032/369990050199923699\) | \(-1301900180773058318532291939\) | \([]\) | \(117573120\) | \(3.9008\) | |
| 244881.bk3 | 244881bk1 | \([0, 0, 1, 24656424, -50490295632]\) | \(471114356703100928/585612268875179\) | \(-2060619517469590594008219\) | \([]\) | \(39191040\) | \(3.3515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 244881.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 244881.bk do not have complex multiplication.Modular form 244881.2.a.bk
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
