Elliptic curve isogeny class with LMFDB label 29400.cl (Cremona label 29400by)

• Label: 29400.cl
• Number of curves: $1$
• Conductor: $29400$
• CM: no
• Rank: $1$

Rank

The elliptic curve 29400.cl1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 29400.cl do not have complex multiplication.

Modular form 29400.2.a.cl

Elliptic curves in class 29400.cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
29400.cl1	29400by1	\([0, 1, 0, -6502708, -6658828912]\)	\(-43061200/2187\)	\(-1544433423907500000000\)	\([]\)	\(2257920\)	\(2.8262\)	\(\Gamma_0(N)\)-optimal