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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 4026.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4026.g1 | 4026h2 | \([1, 1, 1, -562, 4883]\) | \(19632741836833/48626028\) | \(48626028\) | \([2]\) | \(2496\) | \(0.35272\) | |
4026.g2 | 4026h1 | \([1, 1, 1, -22, 131]\) | \(-1180932193/7826544\) | \(-7826544\) | \([2]\) | \(1248\) | \(0.0061506\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4026.g have rank \(0\).
Complex multiplication
The elliptic curves in class 4026.g do not have complex multiplication.Modular form 4026.2.a.g
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.