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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 160080cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160080.b4 | 160080cq1 | \([0, -1, 0, -31, -2114]\) | \(-212629504/121730835\) | \(-1947693360\) | \([2]\) | \(96256\) | \(0.46157\) | \(\Gamma_0(N)\)-optimal |
| 160080.b3 | 160080cq2 | \([0, -1, 0, -2676, -51840]\) | \(8281411334224/100100025\) | \(25625606400\) | \([2, 2]\) | \(192512\) | \(0.80815\) | |
| 160080.b2 | 160080cq3 | \([0, -1, 0, -4976, 53040]\) | \(13309205948356/6588322515\) | \(6746442255360\) | \([2]\) | \(385024\) | \(1.1547\) | |
| 160080.b1 | 160080cq4 | \([0, -1, 0, -42696, -3381504]\) | \(8406118281475876/1250625\) | \(1280640000\) | \([2]\) | \(385024\) | \(1.1547\) |
Rank
sage: E.rank()
The elliptic curves in class 160080cq have rank \(1\).
Complex multiplication
The elliptic curves in class 160080cq do not have complex multiplication.Modular form 160080.2.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.
