Elliptic curve isogeny class with Cremona label 234906bg (LMFDB label 234906.bg)

• Label: 234906bg
• Number of curves: $2$
• Conductor: $234906$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 234906bg have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(17\)	\(1 + T\)
\(47\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 234906bg do not have complex multiplication.

Modular form 234906.2.a.bg

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 234906bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
234906.bg2	234906bg1	\([1, 1, 1, -53264, 4723697]\)	\(-142048716869233/500723712\)	\(-58909643993088\)	\([2]\)	\(1179648\)	\(1.5046\)	\(\Gamma_0(N)\)-optimal
234906.bg1	234906bg2	\([1, 1, 1, -852944, 302844401]\)	\(583306826994199153/7210176\)	\(848269996224\)	\([2]\)	\(2359296\)	\(1.8512\)