Elliptic curve isogeny class with Cremona label 129472x (LMFDB label 129472.a)

• Label: 129472x
• Number of curves: $1$
• Conductor: $129472$
• CM: no
• Rank: $0$

Rank

The elliptic curve 129472x1 has rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 129472x do not have complex multiplication.

Modular form 129472.2.a.x

Elliptic curves in class 129472x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
129472.a1	129472x1	\([0, 0, 0, -216172, -6681680]\)	\(610929/343\)	\(627227964804431872\)	\([]\)	\(3760128\)	\(2.1052\)	\(\Gamma_0(N)\)-optimal