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SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 430950.fn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.fn1 | 430950fn4 | \([1, 1, 1, -785938, -267949219]\) | \(711882749089/1721250\) | \(129814765488281250\) | \([2]\) | \(7077888\) | \(2.1626\) | |
430950.fn2 | 430950fn3 | \([1, 1, 1, -701438, 224854781]\) | \(506071034209/2505630\) | \(188971834916718750\) | \([2]\) | \(7077888\) | \(2.1626\) | \(\Gamma_0(N)\)-optimal* |
430950.fn3 | 430950fn2 | \([1, 1, 1, -67688, -760219]\) | \(454756609/260100\) | \(19616453451562500\) | \([2, 2]\) | \(3538944\) | \(1.8160\) | \(\Gamma_0(N)\)-optimal* |
430950.fn4 | 430950fn1 | \([1, 1, 1, 16812, -84219]\) | \(6967871/4080\) | \(-307709073750000\) | \([2]\) | \(1769472\) | \(1.4694\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 430950.fn have rank \(0\).
Complex multiplication
The elliptic curves in class 430950.fn do not have complex multiplication.Modular form 430950.2.a.fn
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.