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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 38646q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38646.q1 | 38646q1 | \([1, -1, 1, -1360262, 609766165]\) | \(14141641322151794907/32376123526144\) | \(637259239365092352\) | \([2]\) | \(921600\) | \(2.2976\) | \(\Gamma_0(N)\)-optimal |
| 38646.q2 | 38646q2 | \([1, -1, 1, -872102, 1053015445]\) | \(-3726780377767300827/22169935588208416\) | \(-436370842182706252128\) | \([2]\) | \(1843200\) | \(2.6442\) |
Rank
sage: E.rank()
The elliptic curves in class 38646q have rank \(0\).
Complex multiplication
The elliptic curves in class 38646q do not have complex multiplication.Modular form 38646.2.a.q
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.
