Properties

Label 1050p
Number of curves $4$
Conductor $1050$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1050p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.q3 1050p1 \([1, 0, 0, -88, -208]\) \(4826809/1680\) \(26250000\) \([2]\) \(384\) \(0.12515\) \(\Gamma_0(N)\)-optimal
1050.q2 1050p2 \([1, 0, 0, -588, 5292]\) \(1439069689/44100\) \(689062500\) \([2, 2]\) \(768\) \(0.47173\)  
1050.q1 1050p3 \([1, 0, 0, -9338, 346542]\) \(5763259856089/5670\) \(88593750\) \([2]\) \(1536\) \(0.81830\)  
1050.q4 1050p4 \([1, 0, 0, 162, 18042]\) \(30080231/9003750\) \(-140683593750\) \([2]\) \(1536\) \(0.81830\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1050p have rank \(0\).

Complex multiplication

The elliptic curves in class 1050p do not have complex multiplication.

Modular form 1050.2.a.p

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