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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 110110.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 110110.bo1 | 110110bs4 | \([1, 0, 0, -9557300981, 359532709308961]\) | \(54497099771831721530744218729/16209843781074944000000\) | \(28716727058644908867584000000\) | \([2]\) | \(174182400\) | \(4.4390\) | |
| 110110.bo2 | 110110bs3 | \([1, 0, 0, -675862261, 4046019389985]\) | \(19272683606216463573689449/7161126378530668544000\) | \(12686372208276169696477184000\) | \([2]\) | \(87091200\) | \(4.0925\) | |
| 110110.bo3 | 110110bs2 | \([1, 0, 0, -318610366, -1550575760700]\) | \(2019051077229077416165369/582160888682835862400\) | \(1031333526115853383229206400\) | \([2]\) | \(58060800\) | \(3.8897\) | |
| 110110.bo4 | 110110bs1 | \([1, 0, 0, -292048446, -1920801114044]\) | \(1555006827939811751684089/221961497899581440\) | \(393218333180480395427840\) | \([2]\) | \(29030400\) | \(3.5432\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 110110.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 110110.bo do not have complex multiplication.Modular form 110110.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
