Elliptic curve isogeny class with Cremona label 29008k (LMFDB label 29008.a)

• Label: 29008k
• Number of curves: $1$
• Conductor: $29008$
• CM: no
• Rank: $1$

Rank

The elliptic curve 29008k1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(37\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 29008k do not have complex multiplication.

Modular form 29008.2.a.k

Elliptic curves in class 29008k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
29008.a1	29008k1	\([0, 0, 0, -784, 5488]\)	\(110592/37\)	\(17829941248\)	\([]\)	\(30240\)	\(0.66956\)	\(\Gamma_0(N)\)-optimal