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Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 1050.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.j1 1050j2 \([1, 0, 1, -351, -2702]\) \(-7620530425/526848\) \(-329280000\) \([]\) \(648\) \(0.38532\)  
1050.j2 1050j1 \([1, 0, 1, 24, -2]\) \(2595575/1512\) \(-945000\) \([3]\) \(216\) \(-0.16399\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1050.2.a.j

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.