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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 40560cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.cp3 | 40560cq1 | \([0, 1, 0, -36560, -2622060]\) | \(273359449/9360\) | \(185052906455040\) | \([2]\) | \(129024\) | \(1.5095\) | \(\Gamma_0(N)\)-optimal |
| 40560.cp2 | 40560cq2 | \([0, 1, 0, -90640, 6874388]\) | \(4165509529/1368900\) | \(27063987569049600\) | \([2, 2]\) | \(258048\) | \(1.8561\) | |
| 40560.cp4 | 40560cq3 | \([0, 1, 0, 260880, 47510100]\) | \(99317171591/106616250\) | \(-2107868262589440000\) | \([4]\) | \(516096\) | \(2.2027\) | |
| 40560.cp1 | 40560cq4 | \([0, 1, 0, -1307440, 574876628]\) | \(12501706118329/2570490\) | \(50820154435215360\) | \([2]\) | \(516096\) | \(2.2027\) |
Rank
sage: E.rank()
The elliptic curves in class 40560cq have rank \(0\).
Complex multiplication
The elliptic curves in class 40560cq do not have complex multiplication.Modular form 40560.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
