Properties

Label 14144.i
Number of curves $2$
Conductor $14144$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 14144.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14144.i1 14144h2 \([0, 1, 0, -8897, -325985]\) \(297141543217/7514\) \(1969750016\) \([2]\) \(18432\) \(0.89134\)  
14144.i2 14144h1 \([0, 1, 0, -577, -4833]\) \(81182737/11492\) \(3012558848\) \([2]\) \(9216\) \(0.54476\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14144.i have rank \(0\).

Complex multiplication

The elliptic curves in class 14144.i do not have complex multiplication.

Modular form 14144.2.a.i

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