Elliptic curve isogeny class with Cremona label 151008b (LMFDB label 151008.be)

• Label: 151008b
• Number of curves: $4$
• Conductor: $151008$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 151008b have rank \(2\).

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.c
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 151008b do not have complex multiplication.

Modular form 151008.2.a.b

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 151008b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
151008.be3	151008b1	\([0, 1, 0, -28354, -1838344]\)	\(22235451328/123201\)	\(13968517552704\)	\([2, 2]\)	\(491520\)	\(1.3651\)	\(\Gamma_0(N)\)-optimal
151008.be2	151008b2	\([0, 1, 0, -44689, 504095]\)	\(1360251712/771147\)	\(5595684661112832\)	\([2]\)	\(983040\)	\(1.7117\)
151008.be4	151008b3	\([0, 1, 0, -12624, -3851784]\)	\(-245314376/6908733\)	\(-6266491874413056\)	\([2]\)	\(983040\)	\(1.7117\)
151008.be1	151008b4	\([0, 1, 0, -453064, -117529348]\)	\(11339065490696/351\)	\(318370770432\)	\([2]\)	\(983040\)	\(1.7117\)