Elliptic curve isogeny class with LMFDB label 51408.y (Cremona label 51408cn)

• Label: 51408.y
• Number of curves: $1$
• Conductor: $51408$
• CM: no
• Rank: $2$

Rank

The elliptic curve 51408.y1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 51408.y do not have complex multiplication.

Modular form 51408.2.a.y

Elliptic curves in class 51408.y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51408.y1	51408cn1	\([0, 0, 0, -843, 9466]\)	\(-599077107/3332\)	\(-368492544\)	\([]\)	\(16128\)	\(0.48668\)	\(\Gamma_0(N)\)-optimal