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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 16720.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16720.bg1 | 16720z2 | \([0, -1, 0, -496, -3840]\) | \(3301293169/218405\) | \(894586880\) | \([2]\) | \(8192\) | \(0.46710\) | |
16720.bg2 | 16720z1 | \([0, -1, 0, -96, 320]\) | \(24137569/5225\) | \(21401600\) | \([2]\) | \(4096\) | \(0.12053\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16720.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 16720.bg do not have complex multiplication.Modular form 16720.2.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.