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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 31200.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31200.bg1 | 31200cj2 | \([0, 1, 0, -6208, -63412]\) | \(26463592/13689\) | \(13689000000000\) | \([2]\) | \(71680\) | \(1.2127\) | |
31200.bg2 | 31200cj1 | \([0, 1, 0, -4958, -135912]\) | \(107850176/117\) | \(14625000000\) | \([2]\) | \(35840\) | \(0.86609\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 31200.bg have rank \(1\).
Complex multiplication
The elliptic curves in class 31200.bg do not have complex multiplication.Modular form 31200.2.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.