Properties

Label 113a
Number of curves $2$
Conductor $113$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 113a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
113.a2 113a1 \([1, 1, 1, 3, -4]\) \(2924207/12769\) \(-12769\) \([2]\) \(6\) \(-0.52960\) \(\Gamma_0(N)\)-optimal
113.a1 113a2 \([1, 1, 1, -2, -2]\) \(912673/113\) \(113\) \([2]\) \(12\) \(-0.87617\)  

Rank

sage: E.rank()
 

The elliptic curves in class 113a have rank \(0\).

Complex multiplication

The elliptic curves in class 113a do not have complex multiplication.

Modular form 113.2.a.a

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