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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 430950dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.dk1 | 430950dk1 | \([1, 0, 1, -14734776, -21764143802]\) | \(2135227170133/832320\) | \(137911514345865000000\) | \([2]\) | \(20127744\) | \(2.8294\) | \(\Gamma_0(N)\)-optimal |
430950.dk2 | 430950dk2 | \([1, 0, 1, -12537776, -28478175802]\) | \(-1315451937493/1353040200\) | \(-224192405508496790625000\) | \([2]\) | \(40255488\) | \(3.1760\) |
Rank
sage: E.rank()
The elliptic curves in class 430950dk have rank \(0\).
Complex multiplication
The elliptic curves in class 430950dk do not have complex multiplication.Modular form 430950.2.a.dk
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.