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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 330330d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
330330.d2 | 330330d1 | \([1, 1, 0, -22178041888, 1271657990714368]\) | \(-906390311946839196100854971335379/339659381598543082240819200\) | \(-452086636907660842462530355200\) | \([2]\) | \(983162880\) | \(4.6573\) | \(\Gamma_0(N)\)-optimal |
330330.d1 | 330330d2 | \([1, 1, 0, -354880578208, 81371190960406912]\) | \(3713576311940579708906737903766338259/521203066947867573360000\) | \(693721282107611740142160000\) | \([2]\) | \(1966325760\) | \(5.0038\) |
Rank
sage: E.rank()
The elliptic curves in class 330330d have rank \(1\).
Complex multiplication
The elliptic curves in class 330330d do not have complex multiplication.Modular form 330330.2.a.d
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.