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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 22848.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22848.cp1 | 22848bc4 | \([0, 1, 0, -325057, 71224223]\) | \(14489843500598257/6246072\) | \(1637370298368\) | \([4]\) | \(147456\) | \(1.6863\) | |
| 22848.cp2 | 22848bc3 | \([0, 1, 0, -43457, -1857633]\) | \(34623662831857/14438442312\) | \(3784951021436928\) | \([2]\) | \(147456\) | \(1.6863\) | |
| 22848.cp3 | 22848bc2 | \([0, 1, 0, -20417, 1096095]\) | \(3590714269297/73410624\) | \(19244154617856\) | \([2, 2]\) | \(73728\) | \(1.3397\) | |
| 22848.cp4 | 22848bc1 | \([0, 1, 0, 63, 51615]\) | \(103823/4386816\) | \(-1149977493504\) | \([2]\) | \(36864\) | \(0.99312\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22848.cp have rank \(1\).
Complex multiplication
The elliptic curves in class 22848.cp do not have complex multiplication.Modular form 22848.2.a.cp
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
