Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1050l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.l2 1050l1 \([1, 1, 1, 612, -219]\) \(2595575/1512\) \(-14765625000\) \([]\) \(1080\) \(0.64073\) \(\Gamma_0(N)\)-optimal
1050.l1 1050l2 \([1, 1, 1, -8763, -337719]\) \(-7620530425/526848\) \(-5145000000000\) \([]\) \(3240\) \(1.1900\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1050.2.a.l

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