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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 76230cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76230.cb3 | 76230cq1 | \([1, -1, 0, -216077769, -1219442836595]\) | \(863913648706111516969/2486234429521920\) | \(3210892129152547663380480\) | \([2]\) | \(24084480\) | \(3.5735\) | \(\Gamma_0(N)\)-optimal |
| 76230.cb2 | 76230cq2 | \([1, -1, 0, -305288649, -116564411507]\) | \(2436531580079063806249/1405478914998681600\) | \(1815130999825670963629670400\) | \([2, 2]\) | \(48168960\) | \(3.9200\) | |
| 76230.cb4 | 76230cq3 | \([1, -1, 0, 1218962871, -932648675315]\) | \(155099895405729262880471/90047655797243760000\) | \(-116293663145677474525123440000\) | \([2]\) | \(96337920\) | \(4.2666\) | |
| 76230.cb1 | 76230cq4 | \([1, -1, 0, -3256914249, 71282668527373]\) | \(2958414657792917260183849/12401051653985258880\) | \(16015560993036433041692814720\) | \([2]\) | \(96337920\) | \(4.2666\) |
Rank
sage: E.rank()
The elliptic curves in class 76230cq have rank \(1\).
Complex multiplication
The elliptic curves in class 76230cq do not have complex multiplication.Modular form 76230.2.a.cq
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.
