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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 65520.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
65520.b1 | 65520bw4 | \([0, 0, 0, -2302803, -1234377198]\) | \(16751080718799363/1529437000000\) | \(123305609097216000000\) | \([2]\) | \(1990656\) | \(2.5943\) | |
65520.b2 | 65520bw2 | \([0, 0, 0, -2249763, -1298832862]\) | \(11387025941627437947/10765300\) | \(1190556057600\) | \([2]\) | \(663552\) | \(2.0450\) | |
65520.b3 | 65520bw3 | \([0, 0, 0, -505683, 116697618]\) | \(177381177331203/29679104000\) | \(2392775901315072000\) | \([2]\) | \(995328\) | \(2.2477\) | |
65520.b4 | 65520bw1 | \([0, 0, 0, -140643, -20284318]\) | \(2781982314427707/2703013040\) | \(298931618119680\) | \([2]\) | \(331776\) | \(1.6984\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 65520.b have rank \(1\).
Complex multiplication
The elliptic curves in class 65520.b do not have complex multiplication.Modular form 65520.2.a.b
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.