Elliptic curve isogeny class with Cremona label 29400z (LMFDB label 29400.bg)

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

Rank

The elliptic curve 29400z1 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + T + 17 T^{2}\)	1.17.b
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 29400.2.a.z

Elliptic curves in class 29400z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
29400.bg1	29400z1	\([0, -1, 0, -3208, 71212]\)	\(-8318750/27\)	\(-11854080000\)	\([]\)	\(25344\)	\(0.79898\)	\(\Gamma_0(N)\)-optimal