Elliptic curve isogeny class with LMFDB label 459.c (Cremona label 459h)

• Label: 459.c
• Number of curves: $1$
• Conductor: $459$
• CM: no
• Rank: $1$

Elliptic curves in class 459.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
459.c1	459h1	$[1, -1, 1, -2, 28]$	$-27/17$	$-334611$	$[]$	$36$	$-0.26087$	$\Gamma_0(N)$-optimal

Rank

The elliptic curve 459.c1 has rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$3$	$1$
$17$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 + T + 2 T^{2}$	1.2.b
$5$	$1 - T + 5 T^{2}$	1.5.ab
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 + 11 T^{2}$	1.11.a
$13$	$1 + 5 T + 13 T^{2}$	1.13.f
$19$	$1 + T + 19 T^{2}$	1.19.b
$23$	$1 - T + 23 T^{2}$	1.23.ab
$29$	$1 + 9 T + 29 T^{2}$	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 459.c do not have complex multiplication.

Modular form 459.2.a.c