Properties

Label 46410.g
Number of curves $4$
Conductor $46410$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 46410.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46410.g1 46410f4 \([1, 1, 0, -2507978363, 48341976384717]\) \(1744596788171434949302427839201849/9588363813082031250000\) \(9588363813082031250000\) \([2]\) \(25952256\) \(3.8319\)  
46410.g2 46410f3 \([1, 1, 0, -215146843, 142578285613]\) \(1101358349464662961278219354169/628567168199833707765102000\) \(628567168199833707765102000\) \([2]\) \(25952256\) \(3.8319\)  
46410.g3 46410f2 \([1, 1, 0, -156836843, 754401791613]\) \(426646307804307769001905914169/998470877001641316000000\) \(998470877001641316000000\) \([2, 2]\) \(12976128\) \(3.4853\)  
46410.g4 46410f1 \([1, 1, 0, -6246123, 20452740477]\) \(-26949791983733109138764089/165161952797784563712000\) \(-165161952797784563712000\) \([2]\) \(6488064\) \(3.1388\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46410.g have rank \(0\).

Complex multiplication

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

Modular form 46410.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} - q^{13} - q^{14} + q^{15} + q^{16} - q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.