Elliptic curve isogeny class with Cremona label 126400z (LMFDB label 126400.c)

• Label: 126400z
• Number of curves: $1$
• Conductor: $126400$
• CM: no
• Rank: $0$

Rank

The elliptic curve 126400z1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(79\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 126400z do not have complex multiplication.

Modular form 126400.2.a.z

Elliptic curves in class 126400z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
126400.c1	126400z1	\([0, 0, 0, -700, -2000]\)	\(148176/79\)	\(20224000000\)	\([]\)	\(161280\)	\(0.66885\)	\(\Gamma_0(N)\)-optimal