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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 3150.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3150.bo1 | 3150bl3 | \([1, -1, 1, -302405, -63931903]\) | \(268498407453697/252\) | \(2870437500\) | \([2]\) | \(16384\) | \(1.5431\) | |
| 3150.bo2 | 3150bl5 | \([1, -1, 1, -205655, 35603597]\) | \(84448510979617/933897762\) | \(10637679195281250\) | \([2]\) | \(32768\) | \(1.8897\) | |
| 3150.bo3 | 3150bl4 | \([1, -1, 1, -23405, -481903]\) | \(124475734657/63011844\) | \(717744285562500\) | \([2, 2]\) | \(16384\) | \(1.5431\) | |
| 3150.bo4 | 3150bl2 | \([1, -1, 1, -18905, -994903]\) | \(65597103937/63504\) | \(723350250000\) | \([2, 2]\) | \(8192\) | \(1.1966\) | |
| 3150.bo5 | 3150bl1 | \([1, -1, 1, -905, -22903]\) | \(-7189057/16128\) | \(-183708000000\) | \([2]\) | \(4096\) | \(0.84998\) | \(\Gamma_0(N)\)-optimal |
| 3150.bo6 | 3150bl6 | \([1, -1, 1, 86845, -3789403]\) | \(6359387729183/4218578658\) | \(-48052247526281250\) | \([2]\) | \(32768\) | \(1.8897\) |
Rank
sage: E.rank()
The elliptic curves in class 3150.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 3150.bo do not have complex multiplication.Modular form 3150.2.a.bo
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.
\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
