Properties

Label 1122.b
Number of curves $2$
Conductor $1122$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 1122.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1122.b1 1122a2 \([1, 1, 0, -2984, -63840]\) \(2940001530995593/8673562656\) \(8673562656\) \([2]\) \(960\) \(0.77695\)  
1122.b2 1122a1 \([1, 1, 0, -264, -192]\) \(2046931732873/1181672448\) \(1181672448\) \([2]\) \(480\) \(0.43037\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1122.b have rank \(1\).

Complex multiplication

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

Modular form 1122.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.