Elliptic curve isogeny class with Cremona label 20800ce (LMFDB label 20800.e)

• Label: 20800ce
• Number of curves: $1$
• Conductor: $20800$
• CM: no
• Rank: $1$

Rank

The elliptic curve 20800ce1 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 20800ce do not have complex multiplication.

Modular form 20800.2.a.ce

Elliptic curves in class 20800ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20800.e1	20800ce1	\([0, 0, 0, -250, -1250]\)	\(69120/13\)	\(325000000\)	\([]\)	\(9600\)	\(0.35110\)	\(\Gamma_0(N)\)-optimal