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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 7800.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7800.n1 | 7800u3 | \([0, 1, 0, -7608, -251712]\) | \(3044193988/85293\) | \(1364688000000\) | \([2]\) | \(16384\) | \(1.1076\) | |
| 7800.n2 | 7800u2 | \([0, 1, 0, -1108, 8288]\) | \(37642192/13689\) | \(54756000000\) | \([2, 2]\) | \(8192\) | \(0.76098\) | |
| 7800.n3 | 7800u1 | \([0, 1, 0, -983, 11538]\) | \(420616192/117\) | \(29250000\) | \([2]\) | \(4096\) | \(0.41441\) | \(\Gamma_0(N)\)-optimal |
| 7800.n4 | 7800u4 | \([0, 1, 0, 3392, 62288]\) | \(269676572/257049\) | \(-4112784000000\) | \([2]\) | \(16384\) | \(1.1076\) |
Rank
sage: E.rank()
The elliptic curves in class 7800.n have rank \(1\).
Complex multiplication
The elliptic curves in class 7800.n do not have complex multiplication.Modular form 7800.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
