Elliptic curve isogeny class with Cremona label 183920bo (LMFDB label 183920.ch)

• Label: 183920bo
• Number of curves: $2$
• Conductor: $183920$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 183920bo have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 183920bo do not have complex multiplication.

Modular form 183920.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 183920bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
183920.ch2	183920bo1	\([0, -1, 0, -11656, -379344]\)	\(24137569/5225\)	\(37914239897600\)	\([2]\)	\(491520\)	\(1.3195\)	\(\Gamma_0(N)\)-optimal
183920.ch1	183920bo2	\([0, -1, 0, -60056, 5351216]\)	\(3301293169/218405\)	\(1584815227719680\)	\([2]\)	\(983040\)	\(1.6661\)