Properties

Label 114.a
Number of curves $2$
Conductor $114$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 114.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
114.a1 114b1 \([1, 1, 0, -95, -399]\) \(96386901625/18468\) \(18468\) \([2]\) \(20\) \(-0.18069\) \(\Gamma_0(N)\)-optimal
114.a2 114b2 \([1, 1, 0, -85, -473]\) \(-69173457625/42633378\) \(-42633378\) \([2]\) \(40\) \(0.16588\)  

Rank

sage: E.rank()
 

The elliptic curves in class 114.a have rank \(0\).

Complex multiplication

The elliptic curves in class 114.a do not have complex multiplication.

Modular form 114.2.a.a

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