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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 188760.cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 188760.cq1 | 188760i4 | \([0, 1, 0, -6645360, -6595864992]\) | \(8945265872486162/804375\) | \(2918398728960000\) | \([2]\) | \(4423680\) | \(2.4056\) | |
| 188760.cq2 | 188760i3 | \([0, 1, 0, -730880, 73252320]\) | \(11900808771122/6243874065\) | \(22653754946489272320\) | \([2]\) | \(4423680\) | \(2.4056\) | |
| 188760.cq3 | 188760i2 | \([0, 1, 0, -416280, -102672000]\) | \(4397697224644/41409225\) | \(75119583283430400\) | \([2, 2]\) | \(2211840\) | \(2.0590\) | |
| 188760.cq4 | 188760i1 | \([0, 1, 0, -7300, -3862432]\) | \(-94875856/14137695\) | \(-6411722007525120\) | \([4]\) | \(1105920\) | \(1.7125\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 188760.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 188760.cq do not have complex multiplication.Modular form 188760.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
