Elliptic curve isogeny class with LMFDB label 1600.o (Cremona label 1600a)

• Label: 1600.o
• Number of curves: $4$
• Conductor: $1600$
• CM: no
• Rank: $1$

Elliptic curves in class 1600.o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1600.o1	1600a3	$[0, 0, 0, -10700, -426000]$	$132304644/5$	$5120000000$	$[2]$	$1536$	$0.94908$
1600.o2	1600a2	$[0, 0, 0, -700, -6000]$	$148176/25$	$6400000000$	$[2, 2]$	$768$	$0.60250$
1600.o3	1600a1	$[0, 0, 0, -200, 1000]$	$55296/5$	$80000000$	$[2]$	$384$	$0.25593$	$\Gamma_0(N)$-optimal
1600.o4	1600a4	$[0, 0, 0, 1300, -34000]$	$237276/625$	$-640000000000$	$[2]$	$1536$	$0.94908$

Rank

The elliptic curves in class 1600.o have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 3 T^{2}$	1.3.a
$7$	$1 - 4 T + 7 T^{2}$	1.7.ae
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 - 2 T + 29 T^{2}$	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1600.o do not have complex multiplication.

Modular form 1600.2.a.o

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.