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SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 8400bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8400.bh2 | 8400bw1 | \([0, -1, 0, -3073, 110092]\) | \(-1605176213504/1640558367\) | \(-3281116734000\) | \([2]\) | \(16128\) | \(1.0971\) | \(\Gamma_0(N)\)-optimal |
8400.bh1 | 8400bw2 | \([0, -1, 0, -57748, 5358892]\) | \(665567485783184/257298363\) | \(8233547616000\) | \([2]\) | \(32256\) | \(1.4436\) |
Rank
sage: E.rank()
The elliptic curves in class 8400bw have rank \(0\).
Complex multiplication
The elliptic curves in class 8400bw do not have complex multiplication.Modular form 8400.2.a.bw
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.