Elliptic curve isogeny class with LMFDB label 236992.ce (Cremona label 236992ce)

• Label: 236992.ce
• Number of curves: $2$
• Conductor: $236992$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 236992.ce have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1 + T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 236992.ce do not have complex multiplication.

Modular form 236992.2.a.ce

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 236992.ce

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
236992.ce1	236992ce2	\([0, -1, 0, -1151809, -461125695]\)	\(1431644/49\)	\(5783976700260319232\)	\([2]\)	\(3956736\)	\(2.3720\)
236992.ce2	236992ce1	\([0, -1, 0, -178449, 19130129]\)	\(21296/7\)	\(206570596437868544\)	\([2]\)	\(1978368\)	\(2.0254\)	\(\Gamma_0(N)\)-optimal