Properties

Label 19074.x
Number of curves $4$
Conductor $19074$
CM no
Rank $0$
Graph

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

Elliptic curves in class 19074.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19074.x1 19074p3 \([1, 1, 1, -2908791, -1910699799]\) \(112763292123580561/1932612\) \(46648555500228\) \([2]\) \(512000\) \(2.1645\)  
19074.x2 19074p4 \([1, 1, 1, -2905901, -1914682219]\) \(-112427521449300721/466873642818\) \(-11269194767800829442\) \([2]\) \(1024000\) \(2.5110\)  
19074.x3 19074p1 \([1, 1, 1, -13011, 410961]\) \(10091699281/2737152\) \(66068195263488\) \([2]\) \(102400\) \(1.3597\) \(\Gamma_0(N)\)-optimal
19074.x4 19074p2 \([1, 1, 1, 33229, 2722961]\) \(168105213359/228637728\) \(-5518758935603232\) \([2]\) \(204800\) \(1.7063\)  

Rank

sage: E.rank()
 

The elliptic curves in class 19074.x have rank \(0\).

Complex multiplication

The elliptic curves in class 19074.x do not have complex multiplication.

Modular form 19074.2.a.x

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.