Properties

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

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

Elliptic curves in class 1122b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1122.c3 1122b1 \([1, 1, 0, -8279, -264363]\) \(62768149033310713/6915442583808\) \(6915442583808\) \([2]\) \(3840\) \(1.1971\) \(\Gamma_0(N)\)-optimal
1122.c2 1122b2 \([1, 1, 0, -31399, 1848805]\) \(3423676911662954233/483711578981136\) \(483711578981136\) \([2, 2]\) \(7680\) \(1.5437\)  
1122.c1 1122b3 \([1, 1, 0, -483939, 129374577]\) \(12534210458299016895673/315581882565708\) \(315581882565708\) \([2]\) \(15360\) \(1.8903\)  
1122.c4 1122b4 \([1, 1, 0, 51221, 10028185]\) \(14861225463775641287/51859390496937804\) \(-51859390496937804\) \([2]\) \(15360\) \(1.8903\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1122.2.a.b

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.