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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 10560.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10560.bk1 | 10560q5 | \([0, 1, 0, -10949441, -13949212641]\) | \(553808571467029327441/12529687500\) | \(3284582400000000\) | \([2]\) | \(294912\) | \(2.5015\) | |
| 10560.bk2 | 10560q4 | \([0, 1, 0, -756801, 252601119]\) | \(182864522286982801/463015182960\) | \(121376652121866240\) | \([2]\) | \(147456\) | \(2.1549\) | |
| 10560.bk3 | 10560q3 | \([0, 1, 0, -685121, -217605345]\) | \(135670761487282321/643043610000\) | \(168570024099840000\) | \([2, 2]\) | \(147456\) | \(2.1549\) | |
| 10560.bk4 | 10560q6 | \([0, 1, 0, -333121, -440562145]\) | \(-15595206456730321/310672490129100\) | \(-81440929252402790400\) | \([2]\) | \(294912\) | \(2.5015\) | |
| 10560.bk5 | 10560q2 | \([0, 1, 0, -65601, 589599]\) | \(119102750067601/68309049600\) | \(17906807498342400\) | \([2, 2]\) | \(73728\) | \(1.8083\) | |
| 10560.bk6 | 10560q1 | \([0, 1, 0, 16319, 81695]\) | \(1833318007919/1070530560\) | \(-280633163120640\) | \([2]\) | \(36864\) | \(1.4618\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10560.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 10560.bk do not have complex multiplication.Modular form 10560.2.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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
