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Properties

Label 1122.j
Number of curves $4$
Conductor $1122$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1122.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1122.j1 1122m3 \([1, 0, 0, -16594568, -26020768704]\) \(505384091400037554067434625/815656731648\) \(815656731648\) \([2]\) \(34560\) \(2.4409\)  
1122.j2 1122m4 \([1, 0, 0, -16594408, -26021295520]\) \(-505369473241574671219626625/20303219722982711328\) \(-20303219722982711328\) \([2]\) \(69120\) \(2.7875\)  
1122.j3 1122m1 \([1, 0, 0, -205448, -35497920]\) \(959024269496848362625/11151660319506432\) \(11151660319506432\) \([6]\) \(11520\) \(1.8916\) \(\Gamma_0(N)\)-optimal
1122.j4 1122m2 \([1, 0, 0, -41608, -90515392]\) \(-7966267523043306625/3534510366354604032\) \(-3534510366354604032\) \([6]\) \(23040\) \(2.2382\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1122.2.a.j

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.