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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 301392.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301392.j1 | 301392j3 | \([0, 0, 0, -2135470944, -37982948269264]\) | \(-360675992659311050823073792/56219378022244619\) | \(-167870163264374076420096\) | \([]\) | \(151165440\) | \(3.8608\) | |
| 301392.j2 | 301392j2 | \([0, 0, 0, -22975104, -65985170704]\) | \(-449167881463536812032/369990050199923699\) | \(-1104784370056168966434816\) | \([]\) | \(50388480\) | \(3.3115\) | |
| 301392.j3 | 301392j1 | \([0, 0, 0, 2334336, 1470814256]\) | \(471114356703100928/585612268875179\) | \(-1748628865064982491136\) | \([]\) | \(16796160\) | \(2.7622\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 301392.j have rank \(0\).
Complex multiplication
The elliptic curves in class 301392.j do not have complex multiplication.Modular form 301392.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
