Elliptic curve isogeny class with LMFDB label 304704.bk (Cremona label 304704bk)

• Label: 304704.bk
• Number of curves: $4$
• Conductor: $304704$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 304704.bk have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 304704.bk do not have complex multiplication.

Modular form 304704.2.a.bk

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 304704.bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
304704.bk1	304704bk4	\([0, 0, 0, -75268236, -251303058160]\)	\(1666957239793/301806\)	\(8538121601502225629184\)	\([2]\)	\(25952256\)	\(3.2118\)
304704.bk2	304704bk3	\([0, 0, 0, -32609676, 69335742224]\)	\(135559106353/5037138\)	\(142501132408062522949632\)	\([2]\)	\(25952256\)	\(3.2118\)
304704.bk3	304704bk2	\([0, 0, 0, -5186316, -3072897520]\)	\(545338513/171396\)	\(4848809798383979986944\)	\([2, 2]\)	\(12976128\)	\(2.8652\)
304704.bk4	304704bk1	\([0, 0, 0, 907764, -325686256]\)	\(2924207/3312\)	\(-93696807698241159168\)	\([2]\)	\(6488064\)	\(2.5186\)	\(\Gamma_0(N)\)-optimal