Properties

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

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

Elliptic curves in class 1950.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.k1 1950g5 \([1, 0, 1, -225376, -41200852]\) \(81025909800741361/11088090\) \(173251406250\) \([2]\) \(12288\) \(1.5688\)  
1950.k2 1950g4 \([1, 0, 1, -21126, 1179148]\) \(66730743078481/60937500\) \(952148437500\) \([2]\) \(6144\) \(1.2222\)  
1950.k3 1950g3 \([1, 0, 1, -14126, -640852]\) \(19948814692561/231344100\) \(3614751562500\) \([2, 2]\) \(6144\) \(1.2222\)  
1950.k4 1950g6 \([1, 0, 1, -2876, -1630852]\) \(-168288035761/73415764890\) \(-1147121326406250\) \([2]\) \(12288\) \(1.5688\)  
1950.k5 1950g2 \([1, 0, 1, -1626, 9148]\) \(30400540561/15210000\) \(237656250000\) \([2, 2]\) \(3072\) \(0.87564\)  
1950.k6 1950g1 \([1, 0, 1, 374, 1148]\) \(371694959/249600\) \(-3900000000\) \([2]\) \(1536\) \(0.52907\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 1950.k do not have complex multiplication.

Modular form 1950.2.a.k

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

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.