Properties

Label 1122.g
Number of curves $2$
Conductor $1122$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1122.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1122.g1 1122g2 \([1, 1, 1, -1108107, 319580601]\) \(150476552140919246594353/42832838728685592576\) \(42832838728685592576\) \([2]\) \(32448\) \(2.4737\)  
1122.g2 1122g1 \([1, 1, 1, -411787, -97932871]\) \(7722211175253055152433/340131399900069888\) \(340131399900069888\) \([2]\) \(16224\) \(2.1271\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1122.g have rank \(0\).

Complex multiplication

The elliptic curves in class 1122.g do not have complex multiplication.

Modular form 1122.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} - 2q^{7} + q^{8} + q^{9} + 2q^{10} + q^{11} - q^{12} + 4q^{13} - 2q^{14} - 2q^{15} + q^{16} + q^{17} + q^{18} - 2q^{19} + O(q^{20})\)  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.