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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 28050.dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28050.dk1 | 28050dc2 | \([1, 0, 0, -74613, -7830783]\) | \(2940001530995593/8673562656\) | \(135524416500000\) | \([2]\) | \(122880\) | \(1.5817\) | |
28050.dk2 | 28050dc1 | \([1, 0, 0, -6613, -10783]\) | \(2046931732873/1181672448\) | \(18463632000000\) | \([2]\) | \(61440\) | \(1.2351\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28050.dk have rank \(0\).
Complex multiplication
The elliptic curves in class 28050.dk do not have complex multiplication.Modular form 28050.2.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 LMFDB 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 LMFDB labels.