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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 46410.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
46410.j1 | 46410g4 | \([1, 1, 0, -3427203, -2443497147]\) | \(4451879473171293653671609/18353298600\) | \(18353298600\) | \([2]\) | \(737280\) | \(2.0606\) | |
46410.j2 | 46410g2 | \([1, 1, 0, -214203, -38245347]\) | \(1086934883783829079609/69785974440000\) | \(69785974440000\) | \([2, 2]\) | \(368640\) | \(1.7140\) | |
46410.j3 | 46410g3 | \([1, 1, 0, -201203, -43073547]\) | \(-900804278922017287609/277087063526418600\) | \(-277087063526418600\) | \([2]\) | \(737280\) | \(2.0606\) | |
46410.j4 | 46410g1 | \([1, 1, 0, -14203, -525347]\) | \(316892346232279609/66830400000000\) | \(66830400000000\) | \([2]\) | \(184320\) | \(1.3674\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46410.j have rank \(1\).
Complex multiplication
The elliptic curves in class 46410.j do not have complex multiplication.Modular form 46410.2.a.j
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.