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SageMath
sage: E = EllipticCurve("p1")
sage: E.isogeny_class()
Elliptic curves in class 2800.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2800.p1 | 2800a3 | \([0, 0, 0, -7475, -248750]\) | \(1443468546/7\) | \(224000000\) | \([2]\) | \(2048\) | \(0.80269\) | |
| 2800.p2 | 2800a4 | \([0, 0, 0, -1475, 17250]\) | \(11090466/2401\) | \(76832000000\) | \([2]\) | \(2048\) | \(0.80269\) | |
| 2800.p3 | 2800a2 | \([0, 0, 0, -475, -3750]\) | \(740772/49\) | \(784000000\) | \([2, 2]\) | \(1024\) | \(0.45611\) | |
| 2800.p4 | 2800a1 | \([0, 0, 0, 25, -250]\) | \(432/7\) | \(-28000000\) | \([2]\) | \(512\) | \(0.10954\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2800.p have rank \(1\).
Complex multiplication
The elliptic curves in class 2800.p do not have complex multiplication.Modular form 2800.2.a.p
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.
