Elliptic curve isogeny class with Cremona label 399424bo (LMFDB label 399424.bo)

• Label: 399424bo
• Number of curves: $2$
• Conductor: $399424$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 399424bo have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(79\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 399424bo do not have complex multiplication.

Modular form 399424.2.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 399424bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
399424.bo2	399424bo1	\([0, -1, 0, 391103, -194424255]\)	\(103823/316\)	\(-20136758069070659584\)	\([2]\)	\(7188480\)	\(2.3874\)	\(\Gamma_0(N)\)-optimal
399424.bo1	399424bo2	\([0, -1, 0, -3603137, -2254653247]\)	\(81182737/12482\)	\(795401943728291053568\)	\([2]\)	\(14376960\)	\(2.7340\)