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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 116928.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116928.br1 | 116928ck4 | \([0, 0, 0, -117863436, -492511936016]\) | \(947531277805646290177/38367\) | \(7332047880192\) | \([2]\) | \(6291456\) | \(2.8797\) | |
| 116928.br2 | 116928ck6 | \([0, 0, 0, -24462156, 37856255344]\) | \(8471112631466271697/1662662681263647\) | \(317739786473622382313472\) | \([2]\) | \(12582912\) | \(3.2263\) | |
| 116928.br3 | 116928ck3 | \([0, 0, 0, -7507596, -7385292560]\) | \(244883173420511137/18418027974129\) | \(3519739957907302907904\) | \([2, 2]\) | \(6291456\) | \(2.8797\) | |
| 116928.br4 | 116928ck2 | \([0, 0, 0, -7366476, -7695474320]\) | \(231331938231569617/1472026689\) | \(281308681019326464\) | \([2, 2]\) | \(3145728\) | \(2.5331\) | |
| 116928.br5 | 116928ck1 | \([0, 0, 0, -451596, -125063696]\) | \(-53297461115137/4513839183\) | \(-862608101056708608\) | \([2]\) | \(1572864\) | \(2.1865\) | \(\Gamma_0(N)\)-optimal |
| 116928.br6 | 116928ck5 | \([0, 0, 0, 7189044, -32775207824]\) | \(215015459663151503/2552757445339983\) | \(-487839544810628083089408\) | \([2]\) | \(12582912\) | \(3.2263\) |
Rank
sage: E.rank()
The elliptic curves in class 116928.br have rank \(0\).
Complex multiplication
The elliptic curves in class 116928.br do not have complex multiplication.Modular form 116928.2.a.br
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.
