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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 236992bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 236992.bo3 | 236992bo1 | \([0, 0, 0, -124844, 16547120]\) | \(5545233/161\) | \(6247881933848576\) | \([2]\) | \(1351680\) | \(1.8087\) | \(\Gamma_0(N)\)-optimal |
| 236992.bo2 | 236992bo2 | \([0, 0, 0, -294124, -37961040]\) | \(72511713/25921\) | \(1005908991349620736\) | \([2, 2]\) | \(2703360\) | \(2.1553\) | |
| 236992.bo4 | 236992bo3 | \([0, 0, 0, 890836, -266895312]\) | \(2014698447/1958887\) | \(-76017979489135624192\) | \([2]\) | \(5406720\) | \(2.5018\) | |
| 236992.bo1 | 236992bo4 | \([0, 0, 0, -4187564, -3297549008]\) | \(209267191953/55223\) | \(2143023503310061568\) | \([2]\) | \(5406720\) | \(2.5018\) |
Rank
sage: E.rank()
The elliptic curves in class 236992bo have rank \(0\).
Complex multiplication
The elliptic curves in class 236992bo do not have complex multiplication.Modular form 236992.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
