Elliptic curve isogeny class with LMFDB label 448.b (Cremona label 448g)

• Label: 448.b
• Number of curves: $2$
• Conductor: $448$
• CM: no
• Rank: $1$

Elliptic curves in class 448.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
448.b1	448g2	$[0, 1, 0, -33, 31]$	$125000/49$	$1605632$	$[2]$	$64$	$-0.11063$
448.b2	448g1	$[0, 1, 0, 7, 7]$	$8000/7$	$-28672$	$[2]$	$32$	$-0.45720$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 448.b 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 $\mathbb{F}_p$
$3$	$1 + 2 T + 3 T^{2}$	1.3.c
$5$	$1 + 5 T^{2}$	1.5.a
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 + 6 T + 19 T^{2}$	1.19.g
$23$	$1 + 8 T + 23 T^{2}$	1.23.i
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 448.2.a.b

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.