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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 160446bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 160446.a4 | 160446bn1 | \([1, 1, 0, 108335654, 47655976651540]\) | \(79374649975090937760383/553856914190911653543936\) | \(-981191308760965639863948804096\) | \([2]\) | \(283668480\) | \(4.4338\) | \(\Gamma_0(N)\)-optimal |
| 160446.a3 | 160446bn2 | \([1, 1, 0, -19081915866, 994944362433300]\) | \(433744050935826360922067531137/9612122270219882316693504\) | \(17028460941153004936843860639744\) | \([2, 2]\) | \(567336960\) | \(4.7804\) | |
| 160446.a1 | 160446bn3 | \([1, 1, 0, -303668030426, 64408869849277716]\) | \(1748094148784980747354970849498497/887694600425282263291392\) | \(1572605134024013471638761702912\) | \([2]\) | \(1134673920\) | \(5.1269\) | |
| 160446.a2 | 160446bn4 | \([1, 1, 0, -41539825626, -1792140629348076]\) | \(4474676144192042711273397261697/1806328356954994499451382272\) | \(3200020870375547010442590229166592\) | \([2]\) | \(1134673920\) | \(5.1269\) |
Rank
sage: E.rank()
The elliptic curves in class 160446bn have rank \(1\).
Complex multiplication
The elliptic curves in class 160446bn do not have complex multiplication.Modular form 160446.2.a.bn
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.
