Elliptic curve isogeny class with Cremona label 188598x (LMFDB label 188598.c)

• Label: 188598x
• Number of curves: $6$
• Conductor: $188598$
• CM: no
• Rank: $1$

Elliptic curves in class 188598x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
188598.c5	188598x1	$[1, 1, 0, -62904, -5658048]$	$4354703137/352512$	$2228356331129088$	$[2]$	$1204224$	$1.6880$	$\Gamma_0(N)$-optimal
188598.c4	188598x2	$[1, 1, 0, -210824, 30641520]$	$163936758817/30338064$	$191777916747797136$	$[2, 2]$	$2408448$	$2.0345$
188598.c2	188598x3	$[1, 1, 0, -3206204, 2208282780]$	$576615941610337/27060804$	$171061166481831396$	$[2, 2]$	$4816896$	$2.3811$
188598.c6	188598x4	$[1, 1, 0, 417836, 179131012]$	$1276229915423/2927177028$	$-18503748702680838372$	$[2]$	$4816896$	$2.3811$
188598.c1	188598x5	$[1, 1, 0, -51298694, 141397567338]$	$2361739090258884097/5202$	$32883730580898$	$[2]$	$9633792$	$2.7277$
188598.c3	188598x6	$[1, 1, 0, -3039794, 2447946462]$	$-491411892194497/125563633938$	$-793733315873835556962$	$[2]$	$9633792$	$2.7277$

Rank

The elliptic curves in class 188598x have rank $1$.

Complex multiplication

The elliptic curves in class 188598x do not have complex multiplication.

Modular form 188598.2.a.x

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.