Properties

Label 19220.c
Number of curves 4
Conductor 19220
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("19220.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19220.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19220.c1 19220b3 [0, -1, 0, -39721, 3059646] [2] 45360  
19220.c2 19220b4 [0, -1, 0, -34916, 3822680] [2] 90720  
19220.c3 19220b1 [0, -1, 0, -1281, -11710] [2] 15120 \(\Gamma_0(N)\)-optimal
19220.c4 19220b2 [0, -1, 0, 3524, -82824] [2] 30240  

Rank

sage: E.rank()
 

The elliptic curves in class 19220.c have rank \(1\).

Modular form 19220.2.a.c

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} + 2q^{7} + q^{9} - 2q^{13} - 2q^{15} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.