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SageMath
E = EllipticCurve("gx1")
E.isogeny_class()
Elliptic curves in class 119952gx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
119952.r2 | 119952gx1 | \([0, 0, 0, -173019, -26857334]\) | \(3914907891433/135834624\) | \(19874400681590784\) | \([]\) | \(829440\) | \(1.8988\) | \(\Gamma_0(N)\)-optimal |
119952.r1 | 119952gx2 | \([0, 0, 0, -1972299, 1057388794]\) | \(5799070911693913/54760833024\) | \(8012233590580445184\) | \([]\) | \(2488320\) | \(2.4481\) |
Rank
sage: E.rank()
The elliptic curves in class 119952gx have rank \(1\).
Complex multiplication
The elliptic curves in class 119952gx 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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.