Elliptic curve isogeny class with Cremona label 327184k (LMFDB label 327184.k)

• Label: 327184k
• Number of curves: $1$
• Conductor: $327184$
• CM: no
• Rank: $2$

Rank

The elliptic curve 327184k1 has rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 327184k do not have complex multiplication.

Modular form 327184.2.a.k

Elliptic curves in class 327184k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
327184.k1	327184k1	\([0, 1, 0, 48, 196]\)	\(572\)	\(-20939776\)	\([]\)	\(85248\)	\(0.089645\)	\(\Gamma_0(N)\)-optimal