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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 183150.cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
183150.cu1 | 183150ew4 | \([1, -1, 0, -1261670967, -17248817857059]\) | \(19499096390516434897995817/15393430272\) | \(175340791692000000\) | \([2]\) | \(62914560\) | \(3.5133\) | |
183150.cu2 | 183150ew2 | \([1, -1, 0, -78854967, -269494177059]\) | \(4760617885089919932457/133756441657344\) | \(1523569468253184000000\) | \([2, 2]\) | \(31457280\) | \(3.1668\) | |
183150.cu3 | 183150ew3 | \([1, -1, 0, -75686967, -292142209059]\) | \(-4209586785160189454377/801182513521564416\) | \(-9125969568081569676000000\) | \([2]\) | \(62914560\) | \(3.5133\) | |
183150.cu4 | 183150ew1 | \([1, -1, 0, -5126967, -3852193059]\) | \(1308451928740468777/194033737531392\) | \(2210165541568512000000\) | \([2]\) | \(15728640\) | \(2.8202\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 183150.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 183150.cu do not have complex multiplication.Modular form 183150.2.a.cu
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.