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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 227430.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 227430.cu1 | 227430fp3 | \([1, -1, 0, -341754, 76888448]\) | \(4767078987/6860\) | \(6352387959459780\) | \([2]\) | \(2052864\) | \(1.9347\) | |
| 227430.cu2 | 227430fp4 | \([1, -1, 0, -244284, 121588190]\) | \(-1740992427/5882450\) | \(-5447172675236761350\) | \([2]\) | \(4105728\) | \(2.2813\) | |
| 227430.cu3 | 227430fp1 | \([1, -1, 0, -16854, -733772]\) | \(416832723/56000\) | \(71133372072000\) | \([2]\) | \(684288\) | \(1.3854\) | \(\Gamma_0(N)\)-optimal |
| 227430.cu4 | 227430fp2 | \([1, -1, 0, 26466, -3913460]\) | \(1613964717/6125000\) | \(-7780212570375000\) | \([2]\) | \(1368576\) | \(1.7320\) |
Rank
sage: E.rank()
The elliptic curves in class 227430.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 227430.cu do not have complex multiplication.Modular form 227430.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
