Properties

Label 19074d
Number of curves 2
Conductor 19074
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19074.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19074d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19074.b2 19074d1 [1, 1, 0, -2972379, -1970514915] [2] 817152 \(\Gamma_0(N)\)-optimal
19074.b1 19074d2 [1, 1, 0, -47536859, -126171720675] [2] 1634304  

Rank

sage: E.rank()
 

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

Modular form 19074.2.a.b

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.