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SageMath
E = EllipticCurve("fp1")
E.isogeny_class()
Elliptic curves in class 202800fp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 202800.da3 | 202800fp1 | \([0, -1, 0, -914008, -325929488]\) | \(273359449/9360\) | \(2891451663360000000\) | \([2]\) | \(3096576\) | \(2.3142\) | \(\Gamma_0(N)\)-optimal |
| 202800.da2 | 202800fp2 | \([0, -1, 0, -2266008, 863830512]\) | \(4165509529/1368900\) | \(422874805766400000000\) | \([2, 2]\) | \(6193152\) | \(2.6608\) | |
| 202800.da1 | 202800fp3 | \([0, -1, 0, -32686008, 71924950512]\) | \(12501706118329/2570490\) | \(794064913050240000000\) | \([2]\) | \(12386304\) | \(3.0074\) | |
| 202800.da4 | 202800fp4 | \([0, -1, 0, 6521992, 5925718512]\) | \(99317171591/106616250\) | \(-32935441602960000000000\) | \([2]\) | \(12386304\) | \(3.0074\) |
Rank
sage: E.rank()
The elliptic curves in class 202800fp have rank \(0\).
Complex multiplication
The elliptic curves in class 202800fp do not have complex multiplication.Modular form 202800.2.a.fp
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 Cremona 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 Cremona labels.
