Elliptic curve isogeny class with LMFDB label 20800.bc (Cremona label 20800by)

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

Rank

The elliptic curve 20800.bc1 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.b
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 20800.2.a.bc

Elliptic curves in class 20800.bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
20800.bc1	20800by1	\([0, -1, 0, -9783, 367837]\)	\(2588953638400/62748517\)	\(2509940680000\)	\([]\)	\(24192\)	\(1.1636\)	\(\Gamma_0(N)\)-optimal