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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 379050.cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 379050.cq1 | 379050cq4 | \([1, 0, 1, -163817476, -807040913152]\) | \(661397832743623417/443352042\) | \(325904490766234406250\) | \([2]\) | \(58982400\) | \(3.2522\) | |
| 379050.cq2 | 379050cq2 | \([1, 0, 1, -10302226, -12445979152]\) | \(164503536215257/4178071044\) | \(3071266142899527562500\) | \([2, 2]\) | \(29491200\) | \(2.9057\) | |
| 379050.cq3 | 379050cq1 | \([1, 0, 1, -1457726, 396234848]\) | \(466025146777/177366672\) | \(130380802254344250000\) | \([2]\) | \(14745600\) | \(2.5591\) | \(\Gamma_0(N)\)-optimal |
| 379050.cq4 | 379050cq3 | \([1, 0, 1, 1701024, -39717363152]\) | \(740480746823/927484650666\) | \(-681786445383737605406250\) | \([2]\) | \(58982400\) | \(3.2522\) |
Rank
sage: E.rank()
The elliptic curves in class 379050.cq have rank \(1\).
Complex multiplication
The elliptic curves in class 379050.cq do not have complex multiplication.Modular form 379050.2.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 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.
