Elliptic curve isogeny class with Cremona label 281775bz (LMFDB label 281775.bz)

• Label: 281775bz
• Number of curves: $8$
• Conductor: $281775$
• CM: no
• Rank: $0$

Elliptic curves in class 281775bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
281775.bz6	281775bz1	$[1, 0, 1, -794901, 272708323]$	$147281603041/5265$	$1985692199765625$	$[2]$	$2949120$	$2.0244$	$\Gamma_0(N)$-optimal
281775.bz5	281775bz2	$[1, 0, 1, -831026, 246553823]$	$168288035761/27720225$	$10454669431766015625$	$[2, 2]$	$5898240$	$2.3710$
281775.bz7	281775bz3	$[1, 0, 1, 1517099, 1387742573]$	$1023887723039/2798036865$	$-1055278248335643515625$	$[2]$	$11796480$	$2.7176$
281775.bz4	281775bz4	$[1, 0, 1, -3757151, -2568378427]$	$15551989015681/1445900625$	$545320720360634765625$	$[2, 2]$	$11796480$	$2.7176$
281775.bz8	281775bz5	$[1, 0, 1, 4370974, -12159565927]$	$24487529386319/183539412225$	$-69221800418755953515625$	$[2]$	$23592960$	$3.0642$
281775.bz2	281775bz6	$[1, 0, 1, -58703276, -173121150427]$	$59319456301170001/594140625$	$224079848931884765625$	$[2, 2]$	$23592960$	$3.0642$
281775.bz3	281775bz7	$[1, 0, 1, -57294401, -181825180177]$	$-55150149867714721/5950927734375$	$-2244389512538909912109375$	$[2]$	$47185920$	$3.4107$
281775.bz1	281775bz8	$[1, 0, 1, -939250151, -11079574744177]$	$242970740812818720001/24375$	$9193019443359375$	$[2]$	$47185920$	$3.4107$

Rank

The elliptic curves in class 281775bz have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$3$	$1 - T$
$5$	$1$
$13$	$1 + T$
$17$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 - T + 2 T^{2}$	1.2.ab
$7$	$1 + 7 T^{2}$	1.7.a
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 - 8 T + 23 T^{2}$	1.23.ai
$29$	$1 - 2 T + 29 T^{2}$	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 281775bz do not have complex multiplication.

Modular form 281775.2.a.bz

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.

$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 8 & 8 \\ 8 & 4 & 8 & 2 & 4 & 1 & 2 & 2 \\ 16 & 8 & 16 & 4 & 8 & 2 & 1 & 4 \\ 16 & 8 & 16 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.