Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1122.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1122.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1122.i1 1122i1 [1, 0, 0, -904, 10304] [2] 1120 \(\Gamma_0(N)\)-optimal
1122.i2 1122i2 [1, 0, 0, -264, 24768] [2] 2240  

Rank

sage: E.rank()
 

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

Modular form 1122.2.a.i

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

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 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.