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SageMath
E = EllipticCurve("fj1")
E.isogeny_class()
Elliptic curves in class 73920.fj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.fj1 | 73920gr4 | \([0, 1, 0, -17031201, -27058714785]\) | \(2084105208962185000201/31185000\) | \(8174960640000\) | \([2]\) | \(2359296\) | \(2.4812\) | |
| 73920.fj2 | 73920gr3 | \([0, 1, 0, -1154081, -347714721]\) | \(648474704552553481/176469171805080\) | \(46260334573670891520\) | \([2]\) | \(2359296\) | \(2.4812\) | |
| 73920.fj3 | 73920gr2 | \([0, 1, 0, -1064481, -423032481]\) | \(508859562767519881/62240270400\) | \(16315913443737600\) | \([2, 2]\) | \(1179648\) | \(2.1347\) | |
| 73920.fj4 | 73920gr1 | \([0, 1, 0, -60961, -7775905]\) | \(-95575628340361/43812679680\) | \(-11485231102033920\) | \([2]\) | \(589824\) | \(1.7881\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73920.fj have rank \(0\).
Complex multiplication
The elliptic curves in class 73920.fj do not have complex multiplication.Modular form 73920.2.a.fj
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
