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Properties

Label 1950.w
Number of curves $4$
Conductor $1950$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 1950.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.w1 1950v4 \([1, 0, 0, -518488, 143656592]\) \(986551739719628473/111045168\) \(1735080750000\) \([2]\) \(20480\) \(1.7728\)  
1950.w2 1950v3 \([1, 0, 0, -58488, -1851408]\) \(1416134368422073/725251155408\) \(11332049303250000\) \([2]\) \(20480\) \(1.7728\)  
1950.w3 1950v2 \([1, 0, 0, -32488, 2230592]\) \(242702053576633/2554695936\) \(39917124000000\) \([2, 2]\) \(10240\) \(1.4262\)  
1950.w4 1950v1 \([1, 0, 0, -488, 86592]\) \(-822656953/207028224\) \(-3234816000000\) \([2]\) \(5120\) \(1.0796\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1950.w have rank \(1\).

Complex multiplication

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

Modular form 1950.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - 4 q^{7} + q^{8} + q^{9} - 4 q^{11} + q^{12} - q^{13} - 4 q^{14} + q^{16} - 2 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) Copy content 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.