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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 247962.bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 247962.bk1 | 247962bk4 | \([1, 0, 0, -725289758622, -237747167280231228]\) | \(1748094148784980747354970849498497/887694600425282263291392\) | \(21426789668692679974672141506048\) | \([2]\) | \(2723217408\) | \(5.3446\) | |
| 247962.bk2 | 247962bk3 | \([1, 0, 0, -99214955422, 6615094569429188]\) | \(4474676144192042711273397261697/1806328356954994499451382272\) | \(43600375352657809625128201735776768\) | \([2]\) | \(2723217408\) | \(5.3446\) | |
| 247962.bk3 | 247962bk2 | \([1, 0, 0, -45575815582, -3672581344871740]\) | \(433744050935826360922067531137/9612122270219882316693504\) | \(232013264533869054591069304651776\) | \([2, 2]\) | \(1361608704\) | \(4.9980\) | |
| 247962.bk4 | 247962bk1 | \([1, 0, 0, 258752098, -175908011132220]\) | \(79374649975090937760383/553856914190911653543936\) | \(-13368759482410209210320849731584\) | \([2]\) | \(680804352\) | \(4.6515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 247962.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 247962.bk do not have complex multiplication.Modular form 247962.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
