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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 7280n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7280.t4 | 7280n1 | \([0, -1, 0, -3736, -86544]\) | \(1408317602329/2153060\) | \(8818933760\) | \([2]\) | \(6912\) | \(0.80799\) | \(\Gamma_0(N)\)-optimal |
| 7280.t3 | 7280n2 | \([0, -1, 0, -4856, -29200]\) | \(3092354182009/1689383150\) | \(6919713382400\) | \([2]\) | \(13824\) | \(1.1546\) | |
| 7280.t2 | 7280n3 | \([0, -1, 0, -15176, 638960]\) | \(94376601570889/12235496000\) | \(50116591616000\) | \([2]\) | \(20736\) | \(1.3573\) | |
| 7280.t1 | 7280n4 | \([0, -1, 0, -234696, 43840496]\) | \(349046010201856969/7245875000\) | \(29679104000000\) | \([2]\) | \(41472\) | \(1.7039\) |
Rank
sage: E.rank()
The elliptic curves in class 7280n have rank \(1\).
Complex multiplication
The elliptic curves in class 7280n do not have complex multiplication.Modular form 7280.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
