Properties

Label 40344.c
Number of curves $6$
Conductor $40344$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40344.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40344.c1 40344g6 \([0, 1, 0, -646064, -200091360]\) \(3065617154/9\) \(87553921370112\) \([2]\) \(276480\) \(1.9046\)  
40344.c2 40344g4 \([0, 1, 0, -108144, 13651152]\) \(28756228/3\) \(14592320228352\) \([2]\) \(138240\) \(1.5580\)  
40344.c3 40344g3 \([0, 1, 0, -40904, -3051264]\) \(1556068/81\) \(393992646165504\) \([2, 2]\) \(138240\) \(1.5580\)  
40344.c4 40344g2 \([0, 1, 0, -7284, 176256]\) \(35152/9\) \(10944240171264\) \([2, 2]\) \(69120\) \(1.2114\)  
40344.c5 40344g1 \([0, 1, 0, 1121, 18242]\) \(2048/3\) \(-228005003568\) \([2]\) \(34560\) \(0.86486\) \(\Gamma_0(N)\)-optimal
40344.c6 40344g5 \([0, 1, 0, 26336, -12034528]\) \(207646/6561\) \(-63826808678811648\) \([2]\) \(276480\) \(1.9046\)  

Rank

sage: E.rank()
 

The elliptic curves in class 40344.c have rank \(1\).

Complex multiplication

The elliptic curves in class 40344.c do not have complex multiplication.

Modular form 40344.2.a.c

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.