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SageMath
E = EllipticCurve("fs1")
E.isogeny_class()
Elliptic curves in class 35280fs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.dn7 | 35280fs1 | \([0, 0, 0, 1481613, -523061966]\) | \(1023887723039/928972800\) | \(-326346316064804044800\) | \([2]\) | \(1179648\) | \(2.6235\) | \(\Gamma_0(N)\)-optimal |
| 35280.dn6 | 35280fs2 | \([0, 0, 0, -7550067, -4683053774]\) | \(135487869158881/51438240000\) | \(18070152461791395840000\) | \([2, 2]\) | \(2359296\) | \(2.9701\) | |
| 35280.dn5 | 35280fs3 | \([0, 0, 0, -53272947, 146321329714]\) | \(47595748626367201/1215506250000\) | \(427004953041945600000000\) | \([2, 2]\) | \(4718592\) | \(3.3167\) | |
| 35280.dn4 | 35280fs4 | \([0, 0, 0, -106334067, -421926912974]\) | \(378499465220294881/120530818800\) | \(42342239393504767180800\) | \([2]\) | \(4718592\) | \(3.3167\) | |
| 35280.dn8 | 35280fs5 | \([0, 0, 0, 8960973, 467734632946]\) | \(226523624554079/269165039062500\) | \(-94557148402500000000000000\) | \([2]\) | \(9437184\) | \(3.6633\) | |
| 35280.dn2 | 35280fs6 | \([0, 0, 0, -847072947, 9489188569714]\) | \(191342053882402567201/129708022500\) | \(45566172989053839360000\) | \([2, 2]\) | \(9437184\) | \(3.6633\) | |
| 35280.dn3 | 35280fs7 | \([0, 0, 0, -841780947, 9613604548114]\) | \(-187778242790732059201/4984939585440150\) | \(-1751199464089803747975782400\) | \([2]\) | \(18874368\) | \(4.0098\) | |
| 35280.dn1 | 35280fs8 | \([0, 0, 0, -13553164947, 607308275951314]\) | \(783736670177727068275201/360150\) | \(126519986086502400\) | \([2]\) | \(18874368\) | \(4.0098\) |
Rank
sage: E.rank()
The elliptic curves in class 35280fs have rank \(1\).
Complex multiplication
The elliptic curves in class 35280fs do not have complex multiplication.Modular form 35280.2.a.fs
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
