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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 5775.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5775.f1 | 5775p3 | \([1, 0, 0, -53088, -4661583]\) | \(1058993490188089/13182390375\) | \(205974849609375\) | \([2]\) | \(27648\) | \(1.5563\) | |
| 5775.f2 | 5775p2 | \([1, 0, 0, -6213, 72792]\) | \(1697509118089/833765625\) | \(13027587890625\) | \([2, 2]\) | \(13824\) | \(1.2097\) | |
| 5775.f3 | 5775p1 | \([1, 0, 0, -5088, 139167]\) | \(932288503609/779625\) | \(12181640625\) | \([4]\) | \(6912\) | \(0.86317\) | \(\Gamma_0(N)\)-optimal |
| 5775.f4 | 5775p4 | \([1, 0, 0, 22662, 563667]\) | \(82375335041831/56396484375\) | \(-881195068359375\) | \([2]\) | \(27648\) | \(1.5563\) |
Rank
sage: E.rank()
The elliptic curves in class 5775.f have rank \(0\).
Complex multiplication
The elliptic curves in class 5775.f do not have complex multiplication.Modular form 5775.2.a.f
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.
