Properties

Label 46410.j
Number of curves $4$
Conductor $46410$
CM no
Rank $1$
Graph

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Show commands: 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)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - q^{12} - q^{13} - q^{14} + q^{15} + q^{16} + q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.