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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 201586d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
201586.bv2 | 201586d1 | \([1, 0, 0, 186640, -6005504]\) | \(3449795831/2071552\) | \(-431757798318128128\) | \([2]\) | \(4915200\) | \(2.0732\) | \(\Gamma_0(N)\)-optimal |
201586.bv1 | 201586d2 | \([1, 0, 0, -762000, -48694304]\) | \(234770924809/130960928\) | \(27295188312424162592\) | \([2]\) | \(9830400\) | \(2.4197\) |
Rank
sage: E.rank()
The elliptic curves in class 201586d have rank \(2\).
Complex multiplication
The elliptic curves in class 201586d do not have complex multiplication.Modular form 201586.2.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.