Elliptic curve isogeny class with Cremona label 119130bo (LMFDB label 119130.bm)

• Label: 119130bo
• Number of curves: $4$
• Conductor: $119130$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 119130bo have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(11\)	\(1 + T\)
\(19\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 119130bo do not have complex multiplication.

Modular form 119130.2.a.bo

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 119130bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
119130.bm3	119130bo1	\([1, 0, 0, -503061, 137291985]\)	\(299270638153369/1069200\)	\(50301455965200\)	\([2]\)	\(967680\)	\(1.8471\)	\(\Gamma_0(N)\)-optimal
119130.bm2	119130bo2	\([1, 0, 0, -510281, 133146261]\)	\(312341975961049/17862322500\)	\(840348698718622500\)	\([2, 2]\)	\(1935360\)	\(2.1936\)
119130.bm4	119130bo3	\([1, 0, 0, 366949, 543514455]\)	\(116149984977671/2779502343750\)	\(-130764136503283593750\)	\([2]\)	\(3870720\)	\(2.5402\)
119130.bm1	119130bo4	\([1, 0, 0, -1503031, -542519389]\)	\(7981893677157049/1917731420550\)	\(90221364201156254550\)	\([2]\)	\(3870720\)	\(2.5402\)