Elliptic curve isogeny class with LMFDB label 92736.ef (Cremona label 92736em)

• Label: 92736.ef
• Number of curves: $2$
• Conductor: $92736$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 92736.ef have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 2 T + 11 T^{2}\)	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
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 92736.ef do not have complex multiplication.

Modular form 92736.2.a.ef

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 92736.ef

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
92736.ef1	92736em2	\([0, 0, 0, -96204, 10869392]\)	\(1030541881826/62236321\)	\(5946773079195648\)	\([2]\)	\(368640\)	\(1.7792\)
92736.ef2	92736em1	\([0, 0, 0, -94764, 11228240]\)	\(1969910093092/7889\)	\(376902844416\)	\([2]\)	\(184320\)	\(1.4327\)	\(\Gamma_0(N)\)-optimal