Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("19074.x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19074.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19074.x1 19074p3 [1, 1, 1, -2908791, -1910699799] [2] 512000  
19074.x2 19074p4 [1, 1, 1, -2905901, -1914682219] [2] 1024000  
19074.x3 19074p1 [1, 1, 1, -13011, 410961] [2] 102400 \(\Gamma_0(N)\)-optimal
19074.x4 19074p2 [1, 1, 1, 33229, 2722961] [2] 204800  

Rank

sage: E.rank()
 

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

Modular form 19074.2.a.x

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

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.