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SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 93600dk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
93600.bn2 | 93600dk1 | \([0, 0, 0, -4125, 101000]\) | \(10648000/117\) | \(85293000000\) | \([2]\) | \(73728\) | \(0.91214\) | \(\Gamma_0(N)\)-optimal |
93600.bn1 | 93600dk2 | \([0, 0, 0, -7500, -88000]\) | \(1000000/507\) | \(23654592000000\) | \([2]\) | \(147456\) | \(1.2587\) |
Rank
sage: E.rank()
The elliptic curves in class 93600dk have rank \(1\).
Complex multiplication
The elliptic curves in class 93600dk do not have complex multiplication.Modular form 93600.2.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.