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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 102850.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
102850.g1 | 102850bw1 | \([1, 0, 1, -999826, -384882852]\) | \(-99829808490625/25432\) | \(-28158962095000\) | \([]\) | \(1123200\) | \(1.9551\) | \(\Gamma_0(N)\)-optimal |
102850.g2 | 102850bw2 | \([1, 0, 1, -848576, -505253652]\) | \(-61032207990625/64254208678\) | \(-71143906362378973750\) | \([]\) | \(3369600\) | \(2.5044\) |
Rank
sage: E.rank()
The elliptic curves in class 102850.g have rank \(0\).
Complex multiplication
The elliptic curves in class 102850.g do not have complex multiplication.Modular form 102850.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.