Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1122.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1122.f1 1122f1 \([1, 1, 1, -9, -9]\) \(81182737/35904\) \(35904\) \([2]\) \(96\) \(-0.43024\) \(\Gamma_0(N)\)-optimal
1122.f2 1122f2 \([1, 1, 1, 31, -25]\) \(3288008303/2517768\) \(-2517768\) \([2]\) \(192\) \(-0.083666\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1122.2.a.f

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