Elliptic curve isogeny class with LMFDB label 204490.bp (Cremona label 204490b)

• Label: 204490.bp
• Number of curves: $1$
• Conductor: $204490$
• CM: no
• Rank: $1$

Rank

The elliptic curve 204490.bp1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 204490.bp do not have complex multiplication.

Modular form 204490.2.a.bp

Elliptic curves in class 204490.bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
204490.bp1	204490b1	\([1, -1, 1, -62506203, -387491786613]\)	\(-3158470573163361/5758438400000\)	\(-49240329473528709401600000\)	\([]\)	\(125798400\)	\(3.6200\)	\(\Gamma_0(N)\)-optimal