Elliptic curve isogeny class with Cremona label 184910j (LMFDB label 184910.bb)

• Label: 184910j
• Number of curves: $2$
• Conductor: $184910$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 184910j have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1 - T\)
\(11\)	\(1 + T\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 184910j do not have complex multiplication.

Modular form 184910.2.a.j

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 184910j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
184910.bb2	184910j1	\([1, 0, 0, 16775, -3374375]\)	\(109902239/1100000\)	\(-5225114665100000\)	\([]\)	\(1408000\)	\(1.6971\)	\(\Gamma_0(N)\)-optimal
184910.bb1	184910j2	\([1, 0, 0, -9985175, -12145388665]\)	\(-23178622194826561/1610510\)	\(-7650090381172910\)	\([]\)	\(7040000\)	\(2.5019\)