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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 38646d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38646.l1 | 38646d1 | \([1, -1, 0, -151140, -22533552]\) | \(14141641322151794907/32376123526144\) | \(874155335205888\) | \([2]\) | \(307200\) | \(1.7483\) | \(\Gamma_0(N)\)-optimal |
38646.l2 | 38646d2 | \([1, -1, 0, -96900, -38968272]\) | \(-3726780377767300827/22169935588208416\) | \(-598588260881627232\) | \([2]\) | \(614400\) | \(2.0949\) |
Rank
sage: E.rank()
The elliptic curves in class 38646d have rank \(0\).
Complex multiplication
The elliptic curves in class 38646d do not have complex multiplication.Modular form 38646.2.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.