Elliptic curve isogeny class with LMFDB label 28224.et (Cremona label 28224fv)

• Label: 28224.et
• Number of curves: $6$
• Conductor: $28224$
• CM: no
• Rank: $0$

Elliptic curves in class 28224.et

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
28224.et1	28224fv6	$[0, 0, 0, -677964, 214860688]$	$3065617154/9$	$101173833105408$	$[2]$	$196608$	$1.9166$
28224.et2	28224fv4	$[0, 0, 0, -113484, -14713328]$	$28756228/3$	$16862305517568$	$[2]$	$98304$	$1.5701$
28224.et3	28224fv3	$[0, 0, 0, -42924, 3265360]$	$1556068/81$	$455282248974336$	$[2, 2]$	$98304$	$1.5701$
28224.et4	28224fv2	$[0, 0, 0, -7644, -192080]$	$35152/9$	$12646729138176$	$[2, 2]$	$49152$	$1.2235$
28224.et5	28224fv1	$[0, 0, 0, 1176, -19208]$	$2048/3$	$-263473523712$	$[2]$	$24576$	$0.87691$	$\Gamma_0(N)$-optimal
28224.et6	28224fv5	$[0, 0, 0, 27636, 12946192]$	$207646/6561$	$-73755724333842432$	$[2]$	$196608$	$1.9166$

Rank

The elliptic curves in class 28224.et have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$7$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 - 2 T + 17 T^{2}$	1.17.ac
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 8 T + 23 T^{2}$	1.23.i
$29$	$1 - 6 T + 29 T^{2}$	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 28224.et do not have complex multiplication.

Modular form 28224.2.a.et

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.