Properties

Label 16744.e
Number of curves $4$
Conductor $16744$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16744.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16744.e1 16744g3 \([0, 0, 0, -15851, -227386]\) \(215062038362754/113550802729\) \(232552043988992\) \([2]\) \(35840\) \(1.4482\)  
16744.e2 16744g2 \([0, 0, 0, -9091, 330990]\) \(81144432781668/740329681\) \(758097593344\) \([2, 2]\) \(17920\) \(1.1017\)  
16744.e3 16744g1 \([0, 0, 0, -9071, 332530]\) \(322440248841552/27209\) \(6965504\) \([4]\) \(8960\) \(0.75509\) \(\Gamma_0(N)\)-optimal
16744.e4 16744g4 \([0, 0, 0, -2651, 790806]\) \(-1006057824354/131332646081\) \(-268969259173888\) \([2]\) \(35840\) \(1.4482\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16744.e have rank \(0\).

Complex multiplication

The elliptic curves in class 16744.e do not have complex multiplication.

Modular form 16744.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.