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Properties

Label 1050o
Number of curves $2$
Conductor $1050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 1050o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.r2 1050o1 \([1, 0, 0, 22, -2748]\) \(46969655/130691232\) \(-3267280800\) \([5]\) \(600\) \(0.50455\) \(\Gamma_0(N)\)-optimal
1050.r1 1050o2 \([1, 0, 0, -109388, -13934358]\) \(-14822892630025/42\) \(-410156250\) \([]\) \(3000\) \(1.3093\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1050.2.a.o

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.