Elliptic curve isogeny class with Cremona label 8280b (LMFDB label 8280.h)

• Label: 8280b
• Number of curves: $2$
• Conductor: $8280$
• CM: no
• Rank: $0$

Elliptic curves in class 8280b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8280.h2	8280b1	$[0, 0, 0, -123, 518]$	$7443468/115$	$3179520$	$[2]$	$1280$	$0.049019$	$\Gamma_0(N)$-optimal
8280.h1	8280b2	$[0, 0, 0, -243, -658]$	$28697814/13225$	$731289600$	$[2]$	$2560$	$0.39559$

Rank

The elliptic curves in class 8280b have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$5$	$1 + T$
$23$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 + 11 T^{2}$	1.11.a
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$19$	$1 + 19 T^{2}$	1.19.a
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8280b do not have complex multiplication.

Modular form 8280.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.