Elliptic curve isogeny class with LMFDB label 650.e (Cremona label 650d)

• Label: 650.e
• Number of curves: $1$
• Conductor: $650$
• CM: no
• Rank: $0$

Rank

The elliptic curve 650.e1 has rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$5$	$1$
$13$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 - T + 3 T^{2}$	1.3.ab
$7$	$1 - 4 T + 7 T^{2}$	1.7.ae
$11$	$1 - T + 11 T^{2}$	1.11.ab
$17$	$1 - 7 T + 17 T^{2}$	1.17.ah
$19$	$1 + 3 T + 19 T^{2}$	1.19.d
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 4 T + 29 T^{2}$	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 650.e do not have complex multiplication.

Modular form 650.2.a.e

Elliptic curves in class 650.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
650.e1	650d1	$[1, 0, 1, 299, 22048]$	$304175/21632$	$-211250000000$	$[]$	$840$	$0.85258$	$\Gamma_0(N)$-optimal