Elliptic curve isogeny class with LMFDB label 23670.i (Cremona label 23670a)

• Label: 23670.i
• Number of curves: $2$
• Conductor: $23670$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 23670.i have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(263\)	\(1 + T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 23670.i do not have complex multiplication.

Modular form 23670.2.a.i

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 23670.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
23670.i1	23670a2	\([1, -1, 0, -36924, -1065520]\)	\(282855913402707/138338000000\)	\(2722906854000000\)	\([2]\)	\(145152\)	\(1.6550\)
23670.i2	23670a1	\([1, -1, 0, -19644, 1053008]\)	\(42592647088467/538624000\)	\(10601736192000\)	\([2]\)	\(72576\)	\(1.3085\)	\(\Gamma_0(N)\)-optimal