Elliptic curve isogeny class with LMFDB label 382347.bm (Cremona label 382347bm)

• Label: 382347.bm
• Number of curves: $1$
• Conductor: $382347$
• CM: no
• Rank: $0$

Rank

The elliptic curve 382347.bm1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 382347.bm do not have complex multiplication.

Modular form 382347.2.a.bm

Elliptic curves in class 382347.bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
382347.bm1	382347bm1	\([0, 0, 1, -584766, 172118000]\)	\(-3671556096/49\)	\(-295131771593883\)	\([]\)	\(2363904\)	\(1.9198\)	\(\Gamma_0(N)\)-optimal