Properties

Label 1850.k
Number of curves $4$
Conductor $1850$
CM no
Rank $1$
Graph

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

Elliptic curves in class 1850.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1850.k1 1850j3 \([1, -1, 1, -9880, -375503]\) \(6825481747209/46250\) \(722656250\) \([2]\) \(1536\) \(0.88123\)  
1850.k2 1850j2 \([1, -1, 1, -630, -5503]\) \(1767172329/136900\) \(2139062500\) \([2, 2]\) \(768\) \(0.53466\)  
1850.k3 1850j1 \([1, -1, 1, -130, 497]\) \(15438249/2960\) \(46250000\) \([4]\) \(384\) \(0.18808\) \(\Gamma_0(N)\)-optimal
1850.k4 1850j4 \([1, -1, 1, 620, -25503]\) \(1689410871/18741610\) \(-292837656250\) \([2]\) \(1536\) \(0.88123\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1850.k have rank \(1\).

Complex multiplication

The elliptic curves in class 1850.k do not have complex multiplication.

Modular form 1850.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.