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SageMath
E = EllipticCurve("gx1")
E.isogeny_class()
Elliptic curves in class 119952.gx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 119952.gx1 | 119952fu2 | \([0, 0, 0, -906843, 63136010]\) | \(234770924809/130960928\) | \(46006316225004699648\) | \([2]\) | \(4423680\) | \(2.4632\) | |
| 119952.gx2 | 119952fu1 | \([0, 0, 0, 222117, 7816970]\) | \(3449795831/2071552\) | \(-727732139990188032\) | \([2]\) | \(2211840\) | \(2.1167\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 119952.gx have rank \(0\).
Complex multiplication
The elliptic curves in class 119952.gx do not have complex multiplication.Modular form 119952.2.a.gx
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.
