Properties

Label 1950.y
Number of curves $4$
Conductor $1950$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1950.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.y1 1950w3 \([1, 0, 0, -12088, -512458]\) \(12501706118329/2570490\) \(40163906250\) \([2]\) \(3072\) \(1.0318\)  
1950.y2 1950w2 \([1, 0, 0, -838, -6208]\) \(4165509529/1368900\) \(21389062500\) \([2, 2]\) \(1536\) \(0.68518\)  
1950.y3 1950w1 \([1, 0, 0, -338, 2292]\) \(273359449/9360\) \(146250000\) \([4]\) \(768\) \(0.33860\) \(\Gamma_0(N)\)-optimal
1950.y4 1950w4 \([1, 0, 0, 2412, -41958]\) \(99317171591/106616250\) \(-1665878906250\) \([2]\) \(3072\) \(1.0318\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1950.2.a.y

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.