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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 44880.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44880.c1 | 44880bp4 | \([0, -1, 0, -1717936, -308020160]\) | \(136894171818794254129/69177425857031250\) | \(283350736310400000000\) | \([2]\) | \(1966080\) | \(2.6170\) | |
| 44880.c2 | 44880bp2 | \([0, -1, 0, -1388816, -628977984]\) | \(72326626749631816849/69403061722500\) | \(284274940815360000\) | \([2, 2]\) | \(983040\) | \(2.2704\) | |
| 44880.c3 | 44880bp1 | \([0, -1, 0, -1388496, -629282880]\) | \(72276643492008825169/66646800\) | \(272985292800\) | \([2]\) | \(491520\) | \(1.9239\) | \(\Gamma_0(N)\)-optimal |
| 44880.c4 | 44880bp3 | \([0, -1, 0, -1064816, -930427584]\) | \(-32597768919523300849/72509045805004050\) | \(-296997051617296588800\) | \([4]\) | \(1966080\) | \(2.6170\) |
Rank
sage: E.rank()
The elliptic curves in class 44880.c have rank \(0\).
Complex multiplication
The elliptic curves in class 44880.c do not have complex multiplication.Modular form 44880.2.a.c
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.
