Elliptic curve isogeny class with Cremona label 209814bo (LMFDB label 209814.be)

• Label: 209814bo
• Number of curves: $2$
• Conductor: $209814$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 209814bo have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(11\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 209814bo do not have complex multiplication.

Modular form 209814.2.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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 209814bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
209814.be2	209814bo1	\([1, 0, 1, -56091005, 162576131672]\)	\(-1579268174113/10077696\)	\(-124539963880065278916096\)	\([]\)	\(52050600\)	\(3.2688\)	\(\Gamma_0(N)\)-optimal
209814.be1	209814bo2	\([1, 0, 1, -4550306885, 118142933727080]\)	\(-843137281012581793/216\)	\(-2669323642834046616\)	\([]\)	\(156151800\)	\(3.8181\)