Elliptic curve isogeny class with Cremona label 177870bo (LMFDB label 177870.hb)

• Label: 177870bo
• Number of curves: $4$
• Conductor: $177870$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 177870bo have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 177870bo do not have complex multiplication.

Modular form 177870.2.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 177870bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
177870.hb3	177870bo1	\([1, 0, 0, -133526, -15847644]\)	\(1263214441/211200\)	\(44018806674796800\)	\([2]\)	\(2211840\)	\(1.9147\)	\(\Gamma_0(N)\)-optimal
177870.hb2	177870bo2	\([1, 0, 0, -607846, 167334740]\)	\(119168121961/10890000\)	\(2269719719169210000\)	\([2, 2]\)	\(4423680\)	\(2.2613\)
177870.hb1	177870bo3	\([1, 0, 0, -9501346, 11271758840]\)	\(455129268177961/4392300\)	\(915453620064914700\)	\([2]\)	\(8847360\)	\(2.6079\)
177870.hb4	177870bo4	\([1, 0, 0, 696534, 788480496]\)	\(179310732119/1392187500\)	\(-290163032280154687500\)	\([2]\)	\(8847360\)	\(2.6079\)