Elliptic curve isogeny class with Cremona label 2800f (LMFDB label 2800.r)

• Label: 2800f
• Number of curves: $1$
• Conductor: $2800$
• CM: no
• Rank: $0$

Rank

The elliptic curve 2800f1 has rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$5$	$1$
$7$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 2 T + 3 T^{2}$	1.3.c
$11$	$1 + T + 11 T^{2}$	1.11.b
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$17$	$1 + 17 T^{2}$	1.17.a
$19$	$1 + 6 T + 19 T^{2}$	1.19.g
$23$	$1 + 3 T + 23 T^{2}$	1.23.d
$29$	$1 + 3 T + 29 T^{2}$	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2800f do not have complex multiplication.

Modular form 2800.2.a.f

Elliptic curves in class 2800f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2800.r1	2800f1	$[0, 0, 0, 625, -9375]$	$172800/343$	$-53593750000$	$[]$	$1440$	$0.74321$	$\Gamma_0(N)$-optimal