Show commands:
SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 221760.cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221760.cq1 | 221760eu4 | \([0, 0, 0, -1223148, -515044528]\) | \(1058993490188089/13182390375\) | \(2519194031456256000\) | \([2]\) | \(4718592\) | \(2.3406\) | |
221760.cq2 | 221760eu2 | \([0, 0, 0, -143148, 8107472]\) | \(1697509118089/833765625\) | \(159335092224000000\) | \([2, 2]\) | \(2359296\) | \(1.9940\) | |
221760.cq3 | 221760eu1 | \([0, 0, 0, -117228, 15437648]\) | \(932288503609/779625\) | \(148988657664000\) | \([2]\) | \(1179648\) | \(1.6475\) | \(\Gamma_0(N)\)-optimal |
221760.cq4 | 221760eu3 | \([0, 0, 0, 522132, 62128208]\) | \(82375335041831/56396484375\) | \(-10777536000000000000\) | \([2]\) | \(4718592\) | \(2.3406\) |
Rank
sage: E.rank()
The elliptic curves in class 221760.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 221760.cq do not have complex multiplication.Modular form 221760.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.