Elliptic curve isogeny class with Cremona label 4998bd (LMFDB label 4998.be)

• Label: 4998bd
• Number of curves: $6$
• Conductor: $4998$
• CM: no
• Rank: $1$

Elliptic curves in class 4998bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
4998.be5	4998bd1	$[1, 1, 1, -1667, -24991]$	$4354703137/352512$	$41472684288$	$[2]$	$6144$	$0.78031$	$\Gamma_0(N)$-optimal
4998.be4	4998bd2	$[1, 1, 1, -5587, 130241]$	$163936758817/30338064$	$3569242891536$	$[2, 2]$	$12288$	$1.1269$
4998.be2	4998bd3	$[1, 1, 1, -84967, 9497081]$	$576615941610337/27060804$	$3183676529796$	$[2, 2]$	$24576$	$1.4735$
4998.be6	4998bd4	$[1, 1, 1, 11073, 776649]$	$1276229915423/2927177028$	$-344379450167172$	$[2]$	$24576$	$1.4735$
4998.be1	4998bd5	$[1, 1, 1, -1359457, 609526973]$	$2361739090258884097/5202$	$612010098$	$[2]$	$49152$	$1.8200$
4998.be3	4998bd6	$[1, 1, 1, -80557, 10532549]$	$-491411892194497/125563633938$	$-14772435969171762$	$[2]$	$49152$	$1.8200$

Rank

The elliptic curves in class 4998bd have rank $1$.

Complex multiplication

The elliptic curves in class 4998bd do not have complex multiplication.

Modular form 4998.2.a.bd

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.