Elliptic curve isogeny class with LMFDB label 50430.w (Cremona label 50430y)

• Label: 50430.w
• Number of curves: $1$
• Conductor: $50430$
• CM: no
• Rank: $1$

Rank

The elliptic curve 50430.w1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 7 T + 13 T^{2}\)	1.13.ah
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 50430.w do not have complex multiplication.

Modular form 50430.2.a.w

Elliptic curves in class 50430.w

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
50430.w1	50430y1	\([1, 0, 0, -1921, 253961]\)	\(-466393214209/16325867520\)	\(-27443783301120\)	\([]\)	\(240240\)	\(1.2589\)	\(\Gamma_0(N)\)-optimal