Elliptic curve isogeny class with LMFDB label 5200.ba (Cremona label 5200be)

• Label: 5200.ba
• Number of curves: $1$
• Conductor: $5200$
• CM: no
• Rank: $1$

Rank

The elliptic curve 5200.ba1 has rank $1$.

L-function data

Bad L-factors:

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

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.b
$17$	$1 + 7 T + 17 T^{2}$	1.17.h
$19$	$1 - 3 T + 19 T^{2}$	1.19.ad
$23$	$1 + 23 T^{2}$	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 5200.ba do not have complex multiplication.

Modular form 5200.2.a.ba

Elliptic curves in class 5200.ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
5200.ba1	5200be1	$[0, 1, 0, 192, -11212]$	$304175/21632$	$-55377920000$	$[]$	$4032$	$0.74101$	$\Gamma_0(N)$-optimal