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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 8550.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.r1 | 8550g4 | \([1, -1, 0, -217692, 39140716]\) | \(100162392144121/23457780\) | \(267198775312500\) | \([2]\) | \(98304\) | \(1.7587\) | |
| 8550.r2 | 8550g3 | \([1, -1, 0, -100692, -11934284]\) | \(9912050027641/311647500\) | \(3549859804687500\) | \([2]\) | \(98304\) | \(1.7587\) | |
| 8550.r3 | 8550g2 | \([1, -1, 0, -15192, 463216]\) | \(34043726521/11696400\) | \(133229306250000\) | \([2, 2]\) | \(49152\) | \(1.4121\) | |
| 8550.r4 | 8550g1 | \([1, -1, 0, 2808, 49216]\) | \(214921799/218880\) | \(-2493180000000\) | \([2]\) | \(24576\) | \(1.0656\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.r have rank \(0\).
Complex multiplication
The elliptic curves in class 8550.r do not have complex multiplication.Modular form 8550.2.a.r
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.
