Elliptic curve isogeny class with LMFDB label 431.a (Cremona label 431a)

• Label: 431.a
• Number of curves: $1$
• Conductor: $431$
• CM: no
• Rank: $1$

Elliptic curves in class 431.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
431.a1	431a1	$[1, 0, 0, 0, -1]$	$-1/431$	$-431$	$[]$	$10$	$-0.81561$	$\Gamma_0(N)$-optimal

Rank

The elliptic curve 431.a1 has rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$431$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 + T + 2 T^{2}$	1.2.b
$3$	$1 - T + 3 T^{2}$	1.3.ab
$5$	$1 - T + 5 T^{2}$	1.5.ab
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 + 5 T + 11 T^{2}$	1.11.f
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 - 5 T + 19 T^{2}$	1.19.af
$23$	$1 + T + 23 T^{2}$	1.23.b
$29$	$1 + 3 T + 29 T^{2}$	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 431.a do not have complex multiplication.

Modular form 431.2.a.a