Elliptic curve isogeny class with LMFDB label 448.d (Cremona label 448a)

• Label: 448.d
• Number of curves: $4$
• Conductor: $448$
• CM: no
• Rank: $1$

Elliptic curves in class 448.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
448.d1	448a4	$[0, 0, 0, -1196, 15920]$	$1443468546/7$	$917504$	$[4]$	$128$	$0.34454$
448.d2	448a3	$[0, 0, 0, -236, -1104]$	$11090466/2401$	$314703872$	$[2]$	$128$	$0.34454$
448.d3	448a2	$[0, 0, 0, -76, 240]$	$740772/49$	$3211264$	$[2, 2]$	$64$	$-0.0020328$
448.d4	448a1	$[0, 0, 0, 4, 16]$	$432/7$	$-114688$	$[2]$	$32$	$-0.34861$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 448.d have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$7$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 3 T^{2}$	1.3.a
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$19$	$1 + 8 T + 19 T^{2}$	1.19.i
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 448.d do not have complex multiplication.

Modular form 448.2.a.d

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.