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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 358974cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 358974.cu4 | 358974cu1 | \([1, -1, 1, -10048856, 10576447067]\) | \(1308451928740468777/194033737531392\) | \(16641521011199607570432\) | \([2]\) | \(35389440\) | \(2.9884\) | \(\Gamma_0(N)\)-optimal |
| 358974.cu2 | 358974cu2 | \([1, -1, 1, -154555736, 739584755291]\) | \(4760617885089919932457/133756441657344\) | \(11471771159713206042624\) | \([2, 2]\) | \(70778880\) | \(3.3350\) | |
| 358974.cu1 | 358974cu3 | \([1, -1, 1, -2472875096, 47332239924827]\) | \(19499096390516434897995817/15393430272\) | \(1320234803313414912\) | \([2]\) | \(141557760\) | \(3.6816\) | |
| 358974.cu3 | 358974cu4 | \([1, -1, 1, -148346456, 801727229531]\) | \(-4209586785160189454377/801182513521564416\) | \(-68714316397774629811950336\) | \([2]\) | \(141557760\) | \(3.6816\) |
Rank
sage: E.rank()
The elliptic curves in class 358974cu have rank \(1\).
Complex multiplication
The elliptic curves in class 358974cu do not have complex multiplication.Modular form 358974.2.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 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.
