Elliptic curve isogeny class with Cremona label 8640bl (LMFDB label 8640.bl)

• Label: 8640bl
• Number of curves: $2$
• Conductor: $8640$
• CM: no
• Rank: $1$

Elliptic curves in class 8640bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8640.bl1	8640bl1	$[0, 0, 0, -132, -584]$	$-9199872/5$	$-138240$	$[]$	$1152$	$-0.064910$	$\Gamma_0(N)$-optimal
8640.bl2	8640bl2	$[0, 0, 0, 108, -2376]$	$6912/125$	$-2519424000$	$[]$	$3456$	$0.48440$

Rank

The elliptic curves in class 8640bl have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$5$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 + 11 T^{2}$	1.11.a
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 - 3 T + 17 T^{2}$	1.17.ad
$19$	$1 - 5 T + 19 T^{2}$	1.19.af
$23$	$1 - 3 T + 23 T^{2}$	1.23.ad
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8640bl do not have complex multiplication.

Modular form 8640.2.a.bl

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.

$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.