Elliptic curve isogeny class with LMFDB label 36400.x (Cremona label 36400o)

• Label: 36400.x
• Number of curves: $1$
• Conductor: $36400$
• CM: no
• Rank: $1$

Rank

The elliptic curve 36400.x1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 36400.x do not have complex multiplication.

Modular form 36400.2.a.x

Elliptic curves in class 36400.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
36400.x1	36400o1	\([0, -1, 0, -208, 2912]\)	\(-31250/91\)	\(-2912000000\)	\([]\)	\(13824\)	\(0.50298\)	\(\Gamma_0(N)\)-optimal