Elliptic curve isogeny class with Cremona label 20400cx (LMFDB label 20400.dc)

• Label: 20400cx
• Number of curves: $6$
• Conductor: $20400$
• CM: no
• Rank: $1$

Elliptic curves in class 20400cx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20400.dc5	20400cx1	$[0, 1, 0, -13608, -571212]$	$4354703137/352512$	$22560768000000$	$[2]$	$49152$	$1.3052$	$\Gamma_0(N)$-optimal
20400.dc4	20400cx2	$[0, 1, 0, -45608, 3076788]$	$163936758817/30338064$	$1941636096000000$	$[2, 2]$	$98304$	$1.6518$
20400.dc2	20400cx3	$[0, 1, 0, -693608, 222100788]$	$576615941610337/27060804$	$1731891456000000$	$[2, 2]$	$196608$	$1.9984$
20400.dc6	20400cx4	$[0, 1, 0, 90392, 18036788]$	$1276229915423/2927177028$	$-187339329792000000$	$[2]$	$196608$	$1.9984$
20400.dc1	20400cx5	$[0, 1, 0, -11097608, 14225884788]$	$2361739090258884097/5202$	$332928000000$	$[2]$	$393216$	$2.3449$
20400.dc3	20400cx6	$[0, 1, 0, -657608, 246220788]$	$-491411892194497/125563633938$	$-8036072572032000000$	$[2]$	$393216$	$2.3449$

Rank

The elliptic curves in class 20400cx have rank $1$.

Complex multiplication

The elliptic curves in class 20400cx do not have complex multiplication.

Modular form 20400.2.a.cx

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.