Properties

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

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

Elliptic curves in class 1122.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1122.l1 1122j2 \([1, 0, 0, -182, 930]\) \(666940371553/37026\) \(37026\) \([2]\) \(192\) \(-0.058012\)  
1122.l2 1122j1 \([1, 0, 0, -12, 12]\) \(192100033/38148\) \(38148\) \([2]\) \(96\) \(-0.40459\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1122.2.a.l

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.