Elliptic curve isogeny class with Cremona label 57600r (LMFDB label 57600.ch)

• Label: 57600r
• Number of curves: $2$
• Conductor: $57600$
• CM: $\Q(\sqrt{-2})$
• Rank: $0$

Elliptic curves in class 57600r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
57600.ch2	57600r1	$[0, 0, 0, -750, -7000]$	$8000$	$5832000000$	$[2]$	$27648$	$0.60348$	$\Gamma_0(N)$-optimal	$-8$
57600.ch1	57600r2	$[0, 0, 0, -3000, 56000]$	$8000$	$373248000000$	$[2]$	$55296$	$0.95005$		$-8$

Rank

The elliptic curves in class 57600r have rank $0$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 + 5 T + 11 T^{2}$	1.11.f
$13$	$1 - 6 T + 13 T^{2}$	1.13.ag
$17$	$1 + 3 T + 17 T^{2}$	1.17.d
$19$	$1 - T + 19 T^{2}$	1.19.ab
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 - 6 T + 29 T^{2}$	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 57600r has complex multiplication by an order in the imaginary quadratic field $\Q(\sqrt{-2})$.

Modular form 57600.2.a.r

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.