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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 234416bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
234416.bg1 | 234416bg1 | \([0, 0, 0, -27244, 562863]\) | \(1188031905792/614810677\) | \(1157309781413968\) | \([2]\) | \(622080\) | \(1.5824\) | \(\Gamma_0(N)\)-optimal |
234416.bg2 | 234416bg2 | \([0, 0, 0, 102361, 4373250]\) | \(3938211778608/2553381961\) | \(-76903125588400384\) | \([2]\) | \(1244160\) | \(1.9290\) |
Rank
sage: E.rank()
The elliptic curves in class 234416bg have rank \(0\).
Complex multiplication
The elliptic curves in class 234416bg do not have complex multiplication.Modular form 234416.2.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 Cremona 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 Cremona labels.