Show commands:
SageMath
E = EllipticCurve("gx1")
E.isogeny_class()
Elliptic curves in class 308550gx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
308550.gx1 | 308550gx1 | \([1, 1, 1, -599013, -178686969]\) | \(858729462625/38148\) | \(1055961078562500\) | \([2]\) | \(4423680\) | \(1.9601\) | \(\Gamma_0(N)\)-optimal |
308550.gx2 | 308550gx2 | \([1, 1, 1, -568763, -197502469]\) | \(-735091890625/181908738\) | \(-5035350403125281250\) | \([2]\) | \(8847360\) | \(2.3067\) |
Rank
sage: E.rank()
The elliptic curves in class 308550gx have rank \(1\).
Complex multiplication
The elliptic curves in class 308550gx do not have complex multiplication.Modular form 308550.2.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 Cremona 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 Cremona labels.