Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1950.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1950.n1 1950q4 \([1, 1, 1, -2163213, 1223706531]\) \(71647584155243142409/10140000\) \(158437500000\) \([2]\) \(30720\) \(2.0020\)  
1950.n2 1950q3 \([1, 1, 1, -155213, 13034531]\) \(26465989780414729/10571870144160\) \(165185471002500000\) \([2]\) \(30720\) \(2.0020\)  
1950.n3 1950q2 \([1, 1, 1, -135213, 19074531]\) \(17496824387403529/6580454400\) \(102819600000000\) \([2, 2]\) \(15360\) \(1.6554\)  
1950.n4 1950q1 \([1, 1, 1, -7213, 386531]\) \(-2656166199049/2658140160\) \(-41533440000000\) \([4]\) \(7680\) \(1.3088\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1950.2.a.n

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.