Elliptic curve isogeny class with Cremona label 149184eg (LMFDB label 149184.bs)

• Label: 149184eg
• Number of curves: $2$
• Conductor: $149184$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 149184eg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(37\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 149184eg do not have complex multiplication.

Modular form 149184.2.a.eg

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 149184eg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
149184.bs2	149184eg1	\([0, 0, 0, 564, 227824]\)	\(415292/469567\)	\(-22433912782848\)	\([2]\)	\(331776\)	\(1.2408\)	\(\Gamma_0(N)\)-optimal
149184.bs1	149184eg2	\([0, 0, 0, -52716, 4554160]\)	\(169556172914/4353013\)	\(415936869433344\)	\([2]\)	\(663552\)	\(1.5874\)