Elliptic curve isogeny class with Cremona label 32976q (LMFDB label 32976.w)

• Label: 32976q
• Number of curves: $1$
• Conductor: $32976$
• CM: no
• Rank: $1$

Rank

The elliptic curve 32976q1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(229\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 32976q do not have complex multiplication.

Modular form 32976.2.a.q

Elliptic curves in class 32976q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
32976.w1	32976q1	\([0, 0, 0, -36, 27]\)	\(442368/229\)	\(2671056\)	\([]\)	\(7392\)	\(-0.074821\)	\(\Gamma_0(N)\)-optimal