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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 4928.bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4928.bc1 | 4928v2 | \([0, -1, 0, -4705, -118239]\) | \(351596839112/14235529\) | \(466469814272\) | \([2]\) | \(12288\) | \(1.0050\) | |
4928.bc2 | 4928v1 | \([0, -1, 0, 135, -6919]\) | \(65939264/5021863\) | \(-20569550848\) | \([2]\) | \(6144\) | \(0.65845\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4928.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 4928.bc do not have complex multiplication.Modular form 4928.2.a.bc
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.