Properties

Label 14440.g
Number of curves $4$
Conductor $14440$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 14440.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14440.g1 14440h3 \([0, 0, 0, -38627, 2921934]\) \(132304644/5\) \(240874910720\) \([2]\) \(27648\) \(1.2700\)  
14440.g2 14440h2 \([0, 0, 0, -2527, 41154]\) \(148176/25\) \(301093638400\) \([2, 2]\) \(13824\) \(0.92343\)  
14440.g3 14440h1 \([0, 0, 0, -722, -6859]\) \(55296/5\) \(3763670480\) \([2]\) \(6912\) \(0.57686\) \(\Gamma_0(N)\)-optimal
14440.g4 14440h4 \([0, 0, 0, 4693, 233206]\) \(237276/625\) \(-30109363840000\) \([2]\) \(27648\) \(1.2700\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14440.g have rank \(0\).

Complex multiplication

The elliptic curves in class 14440.g do not have complex multiplication.

Modular form 14440.2.a.g

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.