Properties

Label 19890.m
Number of curves 4
Conductor 19890
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19890.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19890.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19890.m1 19890l3 [1, -1, 0, -689580, -219859304] [2] 368640  
19890.m2 19890l4 [1, -1, 0, -577980, 168395656] [2] 368640  
19890.m3 19890l2 [1, -1, 0, -57780, -877424] [2, 2] 184320  
19890.m4 19890l1 [1, -1, 0, 14220, -114224] [2] 92160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 19890.m have rank \(0\).

Modular form 19890.2.a.m

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} + 4q^{7} - q^{8} + q^{10} + 4q^{11} + q^{13} - 4q^{14} + q^{16} + q^{17} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.