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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 44688.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44688.j1 | 44688g4 | \([0, -1, 0, -158384, -20080416]\) | \(1823652903746/328593657\) | \(79173048632100864\) | \([2]\) | \(491520\) | \(1.9616\) | |
| 44688.j2 | 44688g2 | \([0, -1, 0, -46664, 3604224]\) | \(93280467172/7800849\) | \(939788374017024\) | \([2, 2]\) | \(245760\) | \(1.6150\) | |
| 44688.j3 | 44688g1 | \([0, -1, 0, -45684, 3773568]\) | \(350104249168/2793\) | \(84119976192\) | \([2]\) | \(122880\) | \(1.2684\) | \(\Gamma_0(N)\)-optimal |
| 44688.j4 | 44688g3 | \([0, -1, 0, 49376, 16435168]\) | \(55251546334/517244049\) | \(-124627446007400448\) | \([2]\) | \(491520\) | \(1.9616\) |
Rank
sage: E.rank()
The elliptic curves in class 44688.j have rank \(0\).
Complex multiplication
The elliptic curves in class 44688.j do not have complex multiplication.Modular form 44688.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
