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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 25872.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25872.j1 | 25872f4 | \([0, -1, 0, -31371384, -47944627632]\) | \(14171198121996897746/4077720290568771\) | \(982506935224576695048192\) | \([2]\) | \(4423680\) | \(3.3101\) | |
| 25872.j2 | 25872f2 | \([0, -1, 0, -28762624, -59356387376]\) | \(21843440425782779332/3100814593569\) | \(373563121785650463744\) | \([2, 2]\) | \(2211840\) | \(2.9635\) | |
| 25872.j3 | 25872f1 | \([0, -1, 0, -28761644, -59360635872]\) | \(87364831012240243408/1760913\) | \(53035431305472\) | \([2]\) | \(1105920\) | \(2.6169\) | \(\Gamma_0(N)\)-optimal |
| 25872.j4 | 25872f3 | \([0, -1, 0, -26169544, -70496259056]\) | \(-8226100326647904626/4152140742401883\) | \(-1000438182303414544521216\) | \([2]\) | \(4423680\) | \(3.3101\) |
Rank
sage: E.rank()
The elliptic curves in class 25872.j have rank \(0\).
Complex multiplication
The elliptic curves in class 25872.j do not have complex multiplication.Modular form 25872.2.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.
