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

• Label: 2304e
• Number of curves: $2$
• Conductor: $2304$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 2304e 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 2304.2.a.e

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.

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

Isogeny graph

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

Elliptic curves in class 2304e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2304.f1	2304e1	\([0, 0, 0, -210, -1168]\)	\(2744000/9\)	\(3359232\)	\([2]\)	\(512\)	\(0.11759\)	\(\Gamma_0(N)\)-optimal
2304.f2	2304e2	\([0, 0, 0, -120, -2176]\)	\(-8000/81\)	\(-1934917632\)	\([2]\)	\(1024\)	\(0.46417\)