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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 79560.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 79560.bk1 | 79560bs4 | \([0, 0, 0, -562467, 162364174]\) | \(26362547147244676/244298925\) | \(182368170316800\) | \([2]\) | \(589824\) | \(1.9001\) | |
| 79560.bk2 | 79560bs2 | \([0, 0, 0, -35967, 2413474]\) | \(27572037674704/2472575625\) | \(461441953440000\) | \([2, 2]\) | \(294912\) | \(1.5535\) | |
| 79560.bk3 | 79560bs1 | \([0, 0, 0, -7842, -224651]\) | \(4572531595264/776953125\) | \(9062381250000\) | \([2]\) | \(147456\) | \(1.2069\) | \(\Gamma_0(N)\)-optimal |
| 79560.bk4 | 79560bs3 | \([0, 0, 0, 40533, 11302774]\) | \(9865576607324/79640206425\) | \(-59451095535436800\) | \([2]\) | \(589824\) | \(1.9001\) |
Rank
sage: E.rank()
The elliptic curves in class 79560.bk have rank \(1\).
Complex multiplication
The elliptic curves in class 79560.bk do not have complex multiplication.Modular form 79560.2.a.bk
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.
