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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 4620.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4620.j1 | 4620j4 | \([0, 1, 0, -49596, 2224980]\) | \(52702650535889104/22020583921875\) | \(5637269484000000\) | \([2]\) | \(31104\) | \(1.7194\) | |
| 4620.j2 | 4620j2 | \([0, 1, 0, -42756, 3388644]\) | \(33766427105425744/9823275\) | \(2514758400\) | \([6]\) | \(10368\) | \(1.1701\) | |
| 4620.j3 | 4620j1 | \([0, 1, 0, -2661, 52740]\) | \(-130287139815424/2250652635\) | \(-36010442160\) | \([6]\) | \(5184\) | \(0.82354\) | \(\Gamma_0(N)\)-optimal |
| 4620.j4 | 4620j3 | \([0, 1, 0, 10299, 260424]\) | \(7549996227362816/6152409907875\) | \(-98438558526000\) | \([2]\) | \(15552\) | \(1.3728\) |
Rank
sage: E.rank()
The elliptic curves in class 4620.j have rank \(0\).
Complex multiplication
The elliptic curves in class 4620.j do not have complex multiplication.Modular form 4620.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
