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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 229320ck
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
229320.l2 | 229320ck1 | \([0, 0, 0, -25350003, -85794962498]\) | \(-553867390580563692/657061767578125\) | \(-2137263940743750000000000\) | \([2]\) | \(31997952\) | \(3.3624\) | \(\Gamma_0(N)\)-optimal |
229320.l1 | 229320ck2 | \([0, 0, 0, -484725003, -4105969337498]\) | \(1936101054887046531846/905403781953125\) | \(5890121600329905120000000\) | \([2]\) | \(63995904\) | \(3.7089\) |
Rank
sage: E.rank()
The elliptic curves in class 229320ck have rank \(0\).
Complex multiplication
The elliptic curves in class 229320ck do not have complex multiplication.Modular form 229320.2.a.ck
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.