Properties

Label 1050.i
Number of curves $6$
Conductor $1050$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1050.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1050.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1050.i1 1050h4 [1, 0, 1, -33601, 2367848] [2] 2048  
1050.i2 1050h5 [1, 0, 1, -22851, -1318652] [2] 4096  
1050.i3 1050h3 [1, 0, 1, -2601, 17848] [2, 2] 2048  
1050.i4 1050h2 [1, 0, 1, -2101, 36848] [2, 2] 1024  
1050.i5 1050h1 [1, 0, 1, -101, 848] [2] 512 \(\Gamma_0(N)\)-optimal
1050.i6 1050h6 [1, 0, 1, 9649, 140348] [2] 4096  

Rank

sage: E.rank()
 

The elliptic curves in class 1050.i have rank \(1\).

Modular form 1050.2.a.i

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.