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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 285912.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 285912.j1 | 285912j3 | \([0, 0, 0, -1534611, 731622094]\) | \(5690357426/891\) | \(62583059453663232\) | \([2]\) | \(3686400\) | \(2.2339\) | |
| 285912.j2 | 285912j2 | \([0, 0, 0, -105051, 9122470]\) | \(3650692/1089\) | \(38245202999460864\) | \([2, 2]\) | \(1843200\) | \(1.8874\) | |
| 285912.j3 | 285912j1 | \([0, 0, 0, -40071, -2976806]\) | \(810448/33\) | \(289736386359552\) | \([2]\) | \(921600\) | \(1.5408\) | \(\Gamma_0(N)\)-optimal |
| 285912.j4 | 285912j4 | \([0, 0, 0, 284829, 60976510]\) | \(36382894/43923\) | \(-3085113041956509696\) | \([2]\) | \(3686400\) | \(2.2339\) |
Rank
sage: E.rank()
The elliptic curves in class 285912.j have rank \(1\).
Complex multiplication
The elliptic curves in class 285912.j do not have complex multiplication.Modular form 285912.2.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.
