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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 5390d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5390.j4 | 5390d1 | \([1, -1, 0, -1430, 220660]\) | \(-2749884201/176619520\) | \(-20779109908480\) | \([2]\) | \(12288\) | \(1.2352\) | \(\Gamma_0(N)\)-optimal |
| 5390.j3 | 5390d2 | \([1, -1, 0, -64150, 6229236]\) | \(248158561089321/1859334400\) | \(218748832825600\) | \([2, 2]\) | \(24576\) | \(1.5818\) | |
| 5390.j2 | 5390d3 | \([1, -1, 0, -107270, -3162300]\) | \(1160306142246441/634128110000\) | \(74604538013390000\) | \([2]\) | \(49152\) | \(1.9283\) | |
| 5390.j1 | 5390d4 | \([1, -1, 0, -1024550, 399416996]\) | \(1010962818911303721/57392720\) | \(6752196115280\) | \([2]\) | \(49152\) | \(1.9283\) |
Rank
sage: E.rank()
The elliptic curves in class 5390d have rank \(0\).
Complex multiplication
The elliptic curves in class 5390d do not have complex multiplication.Modular form 5390.2.a.d
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 Cremona 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 Cremona labels.
