Elliptic curve isogeny class with LMFDB label 129285.y (Cremona label 129285j)

• Label: 129285.y
• Number of curves: $1$
• Conductor: $129285$
• CM: no
• Rank: $1$

Rank

The elliptic curve 129285.y1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(13\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(19\)	\( 1 + 3 T + 19 T^{2}\)	1.19.d
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 129285.y do not have complex multiplication.

Modular form 129285.2.a.y

Elliptic curves in class 129285.y

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
129285.y1	129285j1	\([0, 0, 1, 78, -205]\)	\(11501568/10625\)	\(-48481875\)	\([]\)	\(19968\)	\(0.16198\)	\(\Gamma_0(N)\)-optimal