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SageMath
E = EllipticCurve("gx1")
E.isogeny_class()
Elliptic curves in class 78400.gx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.gx1 | 78400e1 | \([0, 1, 0, -99633, 12078863]\) | \(-177953104/125\) | \(-76832000000000\) | \([]\) | \(331776\) | \(1.6007\) | \(\Gamma_0(N)\)-optimal |
78400.gx2 | 78400e2 | \([0, 1, 0, 96367, 51474863]\) | \(161017136/1953125\) | \(-1200500000000000000\) | \([]\) | \(995328\) | \(2.1500\) |
Rank
sage: E.rank()
The elliptic curves in class 78400.gx have rank \(1\).
Complex multiplication
The elliptic curves in class 78400.gx do not have complex multiplication.Modular form 78400.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.