Elliptic curve isogeny class with LMFDB label 7488.bk (Cremona label 7488bt)

• Label: 7488.bk
• Number of curves: $4$
• Conductor: $7488$
• CM: no
• Rank: $1$

Elliptic curves in class 7488.bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7488.bk1	7488bt4	$[0, 0, 0, -11945964, 15892048208]$	$986551739719628473/111045168$	$21221062075219968$	$[2]$	$245760$	$2.5571$
7488.bk2	7488bt3	$[0, 0, 0, -1347564, -204211888]$	$1416134368422073/725251155408$	$138597654145907294208$	$[2]$	$245760$	$2.5571$
7488.bk3	7488bt2	$[0, 0, 0, -748524, 246985040]$	$242702053576633/2554695936$	$488209996144705536$	$[2, 2]$	$122880$	$2.2105$
7488.bk4	7488bt1	$[0, 0, 0, -11244, 9580880]$	$-822656953/207028224$	$-39563709722394624$	$[2]$	$61440$	$1.8640$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 7488.bk have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$13$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 + 8 T + 19 T^{2}$	1.19.i
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 - 6 T + 29 T^{2}$	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7488.bk do not have complex multiplication.

Modular form 7488.2.a.bk

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.