Elliptic curve isogeny class with LMFDB label 151008.bu (Cremona label 151008bj)

• Label: 151008.bu
• Number of curves: $4$
• Conductor: $151008$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 151008.bu have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.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 151008.bu do not have complex multiplication.

Modular form 151008.2.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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 151008.bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
151008.bu1	151008bj4	\([0, 1, 0, -187832, -31364280]\)	\(807995051144/938223\)	\(851005069364736\)	\([2]\)	\(737280\)	\(1.7772\)
151008.bu2	151008bj2	\([0, 1, 0, -134592, 18803772]\)	\(297275150024/2827539\)	\(2564688803010048\)	\([2]\)	\(737280\)	\(1.7772\)
151008.bu3	151008bj1	\([0, 1, 0, -14802, -218880]\)	\(3163575232/1656369\)	\(187798958208576\)	\([2, 2]\)	\(368640\)	\(1.4306\)	\(\Gamma_0(N)\)-optimal
151008.bu4	151008bj3	\([0, 1, 0, 55983, -1648737]\)	\(2674043072/1712997\)	\(-12430043866386432\)	\([2]\)	\(737280\)	\(1.7772\)