Elliptic curve isogeny class with Cremona label 43264f (LMFDB label 43264.c)

• Label: 43264f
• Number of curves: $2$
• Conductor: $43264$
• CM: $\Q(\sqrt{-2})$
• Rank: $1$

Elliptic curves in class 43264f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
43264.c2	43264f1	$[0, 1, 0, -563, 4369]$	$8000$	$2471326208$	$[2]$	$18816$	$0.53193$	$\Gamma_0(N)$-optimal	$-8$
43264.c1	43264f2	$[0, 1, 0, -2253, -37205]$	$8000$	$158164877312$	$[2]$	$37632$	$0.87850$		$-8$

Rank

The elliptic curves in class 43264f have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$13$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + T + 3 T^{2}$	1.3.b
$5$	$1 + T + 5 T^{2}$	1.5.b
$7$	$1 - 3 T + 7 T^{2}$	1.7.ad
$11$	$1 + 2 T + 11 T^{2}$	1.11.c
$17$	$1 + 3 T + 17 T^{2}$	1.17.d
$19$	$1 + 19 T^{2}$	1.19.a
$23$	$1 - 6 T + 23 T^{2}$	1.23.ag
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 43264f has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-2})$.

Modular form 43264.2.a.f

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.