Elliptic curve isogeny class with Cremona label 2304g (LMFDB label 2304.e)

• Label: 2304g
• Number of curves: $4$
• Conductor: $2304$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 2304g have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 2304g do not have complex multiplication.

Modular form 2304.2.a.g

Isogeny matrix

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 2304g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2304.e3	2304g1	\([0, 0, 0, -66, -200]\)	\(85184/3\)	\(1119744\)	\([2]\)	\(256\)	\(-0.068409\)	\(\Gamma_0(N)\)-optimal
2304.e4	2304g2	\([0, 0, 0, 24, -704]\)	\(64/9\)	\(-214990848\)	\([2]\)	\(512\)	\(0.27816\)
2304.e1	2304g3	\([0, 0, 0, -5826, 171160]\)	\(58591911104/243\)	\(90699264\)	\([2]\)	\(1280\)	\(0.73631\)
2304.e2	2304g4	\([0, 0, 0, -5736, 176704]\)	\(-873722816/59049\)	\(-1410554953728\)	\([2]\)	\(2560\)	\(1.0829\)