Elliptic curve isogeny class with LMFDB label 23400.k (Cremona label 23400bc)

• Label: 23400.k
• Number of curves: $2$
• Conductor: $23400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 23400.k have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 4 T + 23 T^{2}\)	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 23400.k do not have complex multiplication.

Modular form 23400.2.a.k

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 LMFDB numbering.

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

Isogeny graph

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

Elliptic curves in class 23400.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23400.k1	23400bc2	\([0, 0, 0, -1275, 11750]\)	\(530604/169\)	\(73008000000\)	\([2]\)	\(16384\)	\(0.78828\)
23400.k2	23400bc1	\([0, 0, 0, 225, 1250]\)	\(11664/13\)	\(-1404000000\)	\([2]\)	\(8192\)	\(0.44170\)	\(\Gamma_0(N)\)-optimal