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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 35490.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35490.bj1 | 35490bh8 | \([1, 0, 1, -324615204, -2251161314348]\) | \(783736670177727068275201/360150\) | \(1738375261350\) | \([2]\) | \(4718592\) | \(3.0769\) | |
| 35490.bj2 | 35490bh6 | \([1, 0, 1, -20288454, -35175651548]\) | \(191342053882402567201/129708022500\) | \(626075850375202500\) | \([2, 2]\) | \(2359296\) | \(2.7303\) | |
| 35490.bj3 | 35490bh7 | \([1, 0, 1, -20161704, -35636818748]\) | \(-187778242790732059201/4984939585440150\) | \(-24061351255458784981350\) | \([2]\) | \(4718592\) | \(3.0769\) | |
| 35490.bj4 | 35490bh4 | \([1, 0, 1, -2546834, 1563761396]\) | \(378499465220294881/120530818800\) | \(581779240961209200\) | \([2]\) | \(1179648\) | \(2.3838\) | |
| 35490.bj5 | 35490bh3 | \([1, 0, 1, -1275954, -542481548]\) | \(47595748626367201/1215506250000\) | \(5867016507056250000\) | \([2, 2]\) | \(1179648\) | \(2.3838\) | |
| 35490.bj6 | 35490bh2 | \([1, 0, 1, -180834, 17343796]\) | \(135487869158881/51438240000\) | \(248282559776160000\) | \([2, 2]\) | \(589824\) | \(2.0372\) | |
| 35490.bj7 | 35490bh1 | \([1, 0, 1, 35486, 1941812]\) | \(1023887723039/928972800\) | \(-4483974271795200\) | \([2]\) | \(294912\) | \(1.6906\) | \(\Gamma_0(N)\)-optimal |
| 35490.bj8 | 35490bh5 | \([1, 0, 1, 214626, -1733753084]\) | \(226523624554079/269165039062500\) | \(-1299208233032226562500\) | \([2]\) | \(2359296\) | \(2.7303\) |
Rank
sage: E.rank()
The elliptic curves in class 35490.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 35490.bj do not have complex multiplication.Modular form 35490.2.a.bj
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
