Elliptic curve isogeny class with Cremona label 183744n (LMFDB label 183744.be)

• Label: 183744n
• Number of curves: $4$
• Conductor: $183744$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 183744n have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 - T\)
\(29\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 183744n do not have complex multiplication.

Modular form 183744.2.a.n

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 183744n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
183744.be4	183744n1	\([0, 0, 0, 22164, 1894480]\)	\(6300872423/11759616\)	\(-2247297614217216\)	\([2]\)	\(589824\)	\(1.6304\)	\(\Gamma_0(N)\)-optimal
183744.be3	183744n2	\([0, 0, 0, -162156, 19957840]\)	\(2467489596697/527529024\)	\(100812366412775424\)	\([2, 2]\)	\(1179648\)	\(1.9770\)
183744.be1	183744n3	\([0, 0, 0, -2443116, 1469736016]\)	\(8438952173768857/560166552\)	\(107049495142858752\)	\([2]\)	\(2359296\)	\(2.3235\)
183744.be2	183744n4	\([0, 0, 0, -830316, -273765296]\)	\(331273336732057/22285827432\)	\(4258887944877637632\)	\([2]\)	\(2359296\)	\(2.3235\)