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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 22800.cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22800.cd1 | 22800dl4 | \([0, 1, 0, -387008, 92519988]\) | \(100162392144121/23457780\) | \(1501297920000000\) | \([4]\) | \(294912\) | \(1.9026\) | |
| 22800.cd2 | 22800dl3 | \([0, 1, 0, -179008, -28408012]\) | \(9912050027641/311647500\) | \(19945440000000000\) | \([2]\) | \(294912\) | \(1.9026\) | |
| 22800.cd3 | 22800dl2 | \([0, 1, 0, -27008, 1079988]\) | \(34043726521/11696400\) | \(748569600000000\) | \([2, 2]\) | \(147456\) | \(1.5560\) | |
| 22800.cd4 | 22800dl1 | \([0, 1, 0, 4992, 119988]\) | \(214921799/218880\) | \(-14008320000000\) | \([2]\) | \(73728\) | \(1.2094\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 22800.cd have rank \(0\).
Complex multiplication
The elliptic curves in class 22800.cd do not have complex multiplication.Modular form 22800.2.a.cd
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.
