Elliptic curve isogeny class with LMFDB label 32400.a (Cremona label 32400x)

• Label: 32400.a
• Number of curves: $1$
• Conductor: $32400$
• CM: no
• Rank: $2$

Rank

The elliptic curve 32400.a1 has rank \(2\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 5 T + 7 T^{2}\)	1.7.f
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 32400.a do not have complex multiplication.

Modular form 32400.2.a.a

Elliptic curves in class 32400.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
32400.a1	32400x1	\([0, 0, 0, -315, 2250]\)	\(-18522\)	\(-186624000\)	\([]\)	\(16128\)	\(0.34561\)	\(\Gamma_0(N)\)-optimal