Elliptic curve isogeny class with Cremona label 40344g (LMFDB label 40344.c)

• Label: 40344g
• Number of curves: $6$
• Conductor: $40344$
• CM: no
• Rank: $1$

Elliptic curves in class 40344g

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

Rank

The elliptic curves in class 40344g have rank $1$.

Complex multiplication

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

Modular form 40344.2.a.g

Isogeny 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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.