Show commands:
SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 37440cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37440.fi2 | 37440cq1 | \([0, 0, 0, 25908, 1697776]\) | \(40254822716/49359375\) | \(-2358180864000000\) | \([2]\) | \(122880\) | \(1.6358\) | \(\Gamma_0(N)\)-optimal |
37440.fi1 | 37440cq2 | \([0, 0, 0, -154092, 16313776]\) | \(4234737878642/1247410125\) | \(119191893590016000\) | \([2]\) | \(245760\) | \(1.9824\) |
Rank
sage: E.rank()
The elliptic curves in class 37440cq have rank \(0\).
Complex multiplication
The elliptic curves in class 37440cq do not have complex multiplication.Modular form 37440.2.a.cq
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.