Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("1122.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1122d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.d2 1122d1 [1, 0, 1, -547, 4766] [2] 672 \(\Gamma_0(N)\)-optimal
1122.d1 1122d2 [1, 0, 1, -1227, -9650] [2] 1344  

Rank

sage: E.rank()
 

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

Modular form 1122.2.a.d

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.