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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 76440.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76440.bi1 | 76440q4 | \([0, -1, 0, -81160, 8892892]\) | \(490757540836/2142075\) | \(258061293235200\) | \([2]\) | \(442368\) | \(1.6183\) | |
76440.bi2 | 76440q2 | \([0, -1, 0, -7660, -15308]\) | \(1650587344/950625\) | \(28631060640000\) | \([2, 2]\) | \(221184\) | \(1.2717\) | |
76440.bi3 | 76440q1 | \([0, -1, 0, -5455, -152900]\) | \(9538484224/26325\) | \(49553758800\) | \([2]\) | \(110592\) | \(0.92513\) | \(\Gamma_0(N)\)-optimal |
76440.bi4 | 76440q3 | \([0, -1, 0, 30560, -152900]\) | \(26198797244/15234375\) | \(-1835324400000000\) | \([2]\) | \(442368\) | \(1.6183\) |
Rank
sage: E.rank()
The elliptic curves in class 76440.bi have rank \(1\).
Complex multiplication
The elliptic curves in class 76440.bi do not have complex multiplication.Modular form 76440.2.a.bi
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.