Properties

Label 19074.w
Number of curves 2
Conductor 19074
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19074.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19074.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19074.w1 19074t1 [1, 1, 1, -261262, 50884811] [2] 322560 \(\Gamma_0(N)\)-optimal
19074.w2 19074t2 [1, 1, 1, -76302, 121761483] [2] 645120  

Rank

sage: E.rank()
 

The elliptic curves in class 19074.w have rank \(1\).

Modular form 19074.2.a.w

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

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 LMFDB 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 LMFDB labels.