Properties

Label 1950.k
Number of curves $6$
Conductor $1950$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1950.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1950.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1950.k1 1950g5 [1, 0, 1, -225376, -41200852] [2] 12288  
1950.k2 1950g4 [1, 0, 1, -21126, 1179148] [2] 6144  
1950.k3 1950g3 [1, 0, 1, -14126, -640852] [2, 2] 6144  
1950.k4 1950g6 [1, 0, 1, -2876, -1630852] [2] 12288  
1950.k5 1950g2 [1, 0, 1, -1626, 9148] [2, 2] 3072  
1950.k6 1950g1 [1, 0, 1, 374, 1148] [2] 1536 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1950.k have rank \(0\).

Modular form 1950.2.a.k

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 4q^{11} + q^{12} - q^{13} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.