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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 31850.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31850.bg1 | 31850m1 | \([1, 1, 0, -1030250, 402012500]\) | \(65787589563409/10400000\) | \(19117962500000000\) | \([2]\) | \(552960\) | \(2.1346\) | \(\Gamma_0(N)\)-optimal |
31850.bg2 | 31850m2 | \([1, 1, 0, -932250, 481686500]\) | \(-48743122863889/26406250000\) | \(-48541701660156250000\) | \([2]\) | \(1105920\) | \(2.4812\) |
Rank
sage: E.rank()
The elliptic curves in class 31850.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 31850.bg do not have complex multiplication.Modular form 31850.2.a.bg
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.