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SageMath
E = EllipticCurve("bq1")
E.isogeny_class()
Elliptic curves in class 80080.bq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 80080.bq1 | 80080v4 | \([0, -1, 0, -1263775336, 17288283293040]\) | \(54497099771831721530744218729/16209843781074944000000\) | \(66395520127282970624000000\) | \([2]\) | \(34836480\) | \(3.9332\) | |
| 80080.bq2 | 80080v3 | \([0, -1, 0, -89370216, 194581890416]\) | \(19272683606216463573689449/7161126378530668544000\) | \(29331973646461618356224000\) | \([2]\) | \(17418240\) | \(3.5867\) | |
| 80080.bq3 | 80080v2 | \([0, -1, 0, -42130296, -74542793104]\) | \(2019051077229077416165369/582160888682835862400\) | \(2384531000044895692390400\) | \([2]\) | \(11612160\) | \(3.3839\) | |
| 80080.bq4 | 80080v1 | \([0, -1, 0, -38617976, -92346040720]\) | \(1555006827939811751684089/221961497899581440\) | \(909154295396685578240\) | \([2]\) | \(5806080\) | \(3.0374\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 80080.bq have rank \(1\).
Complex multiplication
The elliptic curves in class 80080.bq do not have complex multiplication.Modular form 80080.2.a.bq
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.
