Elliptic curve isogeny class with Cremona label 29766bu (LMFDB label 29766.bp)

• Label: 29766bu
• Number of curves: $2$
• Conductor: $29766$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 29766bu have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(11\)	\(1\)
\(41\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 29766bu do not have complex multiplication.

Modular form 29766.2.a.bu

Isogeny matrix

The \(i,j\) 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.

Elliptic curves in class 29766bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
29766.bp1	29766bu1	\([1, 0, 0, -54921479, 156656618889]\)	\(10341755683137709164937/356992303104\)	\(632433641479225344\)	\([2]\)	\(2150400\)	\(2.9133\)	\(\Gamma_0(N)\)-optimal
29766.bp2	29766bu2	\([1, 0, 0, -54844039, 157120438025]\)	\(-10298071306410575356297/60769798505543808\)	\(-107657405010279694044288\)	\([2]\)	\(4300800\)	\(3.2599\)