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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 426888.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
426888.bg1 | 426888bg1 | \([0, 0, 0, -320166, -61631955]\) | \(55296/7\) | \(459466303216680144\) | \([2]\) | \(4976640\) | \(2.1183\) | \(\Gamma_0(N)\)-optimal |
426888.bg2 | 426888bg2 | \([0, 0, 0, 480249, -320486166]\) | \(11664/49\) | \(-51460225960268176128\) | \([2]\) | \(9953280\) | \(2.4649\) |
Rank
sage: E.rank()
The elliptic curves in class 426888.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 426888.bg do not have complex multiplication.Modular form 426888.2.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.