Elliptic curve isogeny class with Cremona label 244800ip (LMFDB label 244800.ip)

• Label: 244800ip
• Number of curves: $6$
• Conductor: $244800$
• CM: no
• Rank: $1$

Elliptic curves in class 244800ip

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
244800.ip5	244800ip1	$[0, 0, 0, -489900, -122402000]$	$4354703137/352512$	$1052595191808000000$	$[2]$	$3145728$	$2.2011$	$\Gamma_0(N)$-optimal
244800.ip4	244800ip2	$[0, 0, 0, -1641900, 667870000]$	$163936758817/30338064$	$90588973694976000000$	$[2, 2]$	$6291456$	$2.5477$
244800.ip2	244800ip3	$[0, 0, 0, -24969900, 48023710000]$	$576615941610337/27060804$	$80803127771136000000$	$[2, 2]$	$12582912$	$2.8942$
244800.ip6	244800ip4	$[0, 0, 0, 3254100, 3889438000]$	$1276229915423/2927177028$	$-8740503770775552000000$	$[2]$	$12582912$	$2.8942$
244800.ip1	244800ip5	$[0, 0, 0, -399513900, 3073590142000]$	$2361739090258884097/5202$	$15533088768000000$	$[2]$	$25165824$	$3.2408$
244800.ip3	244800ip6	$[0, 0, 0, -23673900, 53231038000]$	$-491411892194497/125563633938$	$-374931001920724992000000$	$[2]$	$25165824$	$3.2408$

Rank

The elliptic curves in class 244800ip have rank $1$.

Complex multiplication

The elliptic curves in class 244800ip do not have complex multiplication.

Modular form 244800.2.a.ip

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.