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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 131760.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
131760.u1 | 131760r3 | \([0, 0, 0, -1037568, -406792528]\) | \(-124110120626946048/305\) | \(-303575040\) | \([]\) | \(777600\) | \(1.7541\) | |
131760.u2 | 131760r1 | \([0, 0, 0, -12768, -561808]\) | \(-2081462648832/28372625\) | \(-3137785344000\) | \([]\) | \(259200\) | \(1.2048\) | \(\Gamma_0(N)\)-optimal |
131760.u3 | 131760r2 | \([0, 0, 0, 45792, -2830032]\) | \(131716841472/119140625\) | \(-9605304000000000\) | \([]\) | \(777600\) | \(1.7541\) |
Rank
sage: E.rank()
The elliptic curves in class 131760.u have rank \(0\).
Complex multiplication
The elliptic curves in class 131760.u do not have complex multiplication.Modular form 131760.2.a.u
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.