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SageMath
E = EllipticCurve("gj1")
E.isogeny_class()
Elliptic curves in class 259920.gj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.gj1 | 259920gj2 | \([0, 0, 0, -2305707, 748550106]\) | \(260549802603/104256800\) | \(542437503666182553600\) | \([2]\) | \(11059200\) | \(2.6767\) | |
| 259920.gj2 | 259920gj1 | \([0, 0, 0, 466773, 84818394]\) | \(2161700757/1848320\) | \(-9616620563610992640\) | \([2]\) | \(5529600\) | \(2.3301\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.gj have rank \(0\).
Complex multiplication
The elliptic curves in class 259920.gj do not have complex multiplication.Modular form 259920.2.a.gj
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
