Properties

Label 1050.g
Number of curves $2$
Conductor $1050$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1050.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1050.g1 1050i1 \([1, 0, 1, -171, 838]\) \(4386781853/27216\) \(3402000\) \([2]\) \(320\) \(0.091347\) \(\Gamma_0(N)\)-optimal
1050.g2 1050i2 \([1, 0, 1, -71, 1838]\) \(-310288733/11573604\) \(-1446700500\) \([2]\) \(640\) \(0.43792\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1050.2.a.g

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.