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Properties

Label 46410.x
Number of curves $2$
Conductor $46410$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 46410.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46410.x1 46410x1 \([1, 0, 1, -29, -28]\) \(2565726409/1206660\) \(1206660\) \([2]\) \(8704\) \(-0.13880\) \(\Gamma_0(N)\)-optimal
46410.x2 46410x2 \([1, 0, 1, 101, -184]\) \(115572468311/82841850\) \(-82841850\) \([2]\) \(17408\) \(0.20777\)  

Rank

sage: E.rank()
 

The elliptic curves in class 46410.x have rank \(1\).

Complex multiplication

The elliptic curves in class 46410.x do not have complex multiplication.

Modular form 46410.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + q^{12} - q^{13} - q^{14} - q^{15} + q^{16} - q^{17} - q^{18} + 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.