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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 92736co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92736.bk5 | 92736co1 | \([0, 0, 0, 72564, -15409424]\) | \(221115865823/664731648\) | \(-127032196174184448\) | \([2]\) | \(786432\) | \(1.9653\) | \(\Gamma_0(N)\)-optimal |
| 92736.bk4 | 92736co2 | \([0, 0, 0, -664716, -178495760]\) | \(169967019783457/26337394944\) | \(5033154553885753344\) | \([2, 2]\) | \(1572864\) | \(2.3119\) | |
| 92736.bk3 | 92736co3 | \([0, 0, 0, -2922636, 1749767920]\) | \(14447092394873377/1439452851984\) | \(275083723825829904384\) | \([2, 2]\) | \(3145728\) | \(2.6584\) | |
| 92736.bk2 | 92736co4 | \([0, 0, 0, -10203276, -12544284944]\) | \(614716917569296417/19093020912\) | \(3648733117113434112\) | \([2]\) | \(3145728\) | \(2.6584\) | |
| 92736.bk6 | 92736co5 | \([0, 0, 0, 3609204, 8461886704]\) | \(27207619911317663/177609314617308\) | \(-33941668588687859908608\) | \([2]\) | \(6291456\) | \(3.0050\) | |
| 92736.bk1 | 92736co6 | \([0, 0, 0, -45581196, 118446524656]\) | \(54804145548726848737/637608031452\) | \(121848792331978801152\) | \([2]\) | \(6291456\) | \(3.0050\) |
Rank
sage: E.rank()
The elliptic curves in class 92736co have rank \(0\).
Complex multiplication
The elliptic curves in class 92736co do not have complex multiplication.Modular form 92736.2.a.co
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
