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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 327990.y
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 327990.y1 | 327990y4 | \([1, 1, 1, -274211011, -1747842838417]\) | \(3833455222908263170009/14910644531250\) | \(8869199098328613281250\) | \([2]\) | \(51609600\) | \(3.4245\) | |
| 327990.y2 | 327990y2 | \([1, 1, 1, -17394841, -26455414141]\) | \(978581759592931129/58281773062500\) | \(34667357806804590562500\) | \([2, 2]\) | \(25804800\) | \(3.0779\) | |
| 327990.y3 | 327990y1 | \([1, 1, 1, -3249221, 1739635643]\) | \(6377838054073849/1489533786000\) | \(886009433330223306000\) | \([2]\) | \(12902400\) | \(2.7313\) | \(\Gamma_0(N)\)-optimal |
| 327990.y4 | 327990y3 | \([1, 1, 1, 13091409, -109268263641]\) | \(417152543917888871/8913566138987250\) | \(-5301997012745543621657250\) | \([2]\) | \(51609600\) | \(3.4245\) |
Rank
sage: E.rank()
The elliptic curves in class 327990.y have rank \(0\).
Complex multiplication
The elliptic curves in class 327990.y do not have complex multiplication.Modular form 327990.2.a.y
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.
