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SageMath
E = EllipticCurve("iu1")
E.isogeny_class()
Elliptic curves in class 388080iu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388080.iu7 | 388080iu1 | \([0, 0, 0, -8273307, -4164314294]\) | \(178272935636041/81841914000\) | \(28750903291885953024000\) | \([2]\) | \(21233664\) | \(3.0042\) | \(\Gamma_0(N)\)-optimal |
| 388080.iu5 | 388080iu2 | \([0, 0, 0, -111149787, -450792264566]\) | \(432288716775559561/270140062500\) | \(94899672216873216000000\) | \([2, 2]\) | \(42467328\) | \(3.3508\) | |
| 388080.iu4 | 388080iu3 | \([0, 0, 0, -336906507, 2380063836346]\) | \(12038605770121350841/757333463040\) | \(266049754842880687472640\) | \([2]\) | \(63700992\) | \(3.5535\) | |
| 388080.iu6 | 388080iu4 | \([0, 0, 0, -90193467, -625974525974]\) | \(-230979395175477481/348191894531250\) | \(-122319127173474000000000000\) | \([2]\) | \(84934656\) | \(3.6974\) | |
| 388080.iu2 | 388080iu5 | \([0, 0, 0, -1778129787, -28859798820566]\) | \(1769857772964702379561/691787250\) | \(243023499222045696000\) | \([2]\) | \(84934656\) | \(3.6974\) | |
| 388080.iu3 | 388080iu6 | \([0, 0, 0, -357227787, 2076760603834]\) | \(14351050585434661561/3001282273281600\) | \(1054344554927819868871065600\) | \([2, 2]\) | \(127401984\) | \(3.9001\) | |
| 388080.iu8 | 388080iu7 | \([0, 0, 0, 769756533, 12535851284026]\) | \(143584693754978072519/276341298967965000\) | \(-97078154381654676741181440000\) | \([2]\) | \(254803968\) | \(4.2467\) | |
| 388080.iu1 | 388080iu8 | \([0, 0, 0, -1809352587, -27793736957126]\) | \(1864737106103260904761/129177711985836360\) | \(45379875949282883739482357760\) | \([2]\) | \(254803968\) | \(4.2467\) |
Rank
sage: E.rank()
The elliptic curves in class 388080iu have rank \(1\).
Complex multiplication
The elliptic curves in class 388080iu do not have complex multiplication.Modular form 388080.2.a.iu
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.
\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
