Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("19074.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19074n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19074.q3 19074n1 [1, 1, 1, -59374478, -174341906485] [2] 3317760 \(\Gamma_0(N)\)-optimal
19074.q4 19074n2 [1, 1, 1, -12024718, -444690096181] [2] 6635520  
19074.q1 19074n3 [1, 1, 1, -4795830158, -127835240812597] [2] 9953280  
19074.q2 19074n4 [1, 1, 1, -4795783918, -127837829105845] [2] 19906560  

Rank

sage: E.rank()
 

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

Modular form 19074.2.a.q

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.