Elliptic curve isogeny class with Cremona label 183744cr (LMFDB label 183744.bh)

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

Rank

The elliptic curves in class 183744cr 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 183744.2.a.cr

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 183744cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
183744.bh4	183744cr1	\([0, 0, 0, 22164, -1894480]\)	\(6300872423/11759616\)	\(-2247297614217216\)	\([2]\)	\(589824\)	\(1.6304\)	\(\Gamma_0(N)\)-optimal
183744.bh3	183744cr2	\([0, 0, 0, -162156, -19957840]\)	\(2467489596697/527529024\)	\(100812366412775424\)	\([2, 2]\)	\(1179648\)	\(1.9770\)
183744.bh2	183744cr3	\([0, 0, 0, -830316, 273765296]\)	\(331273336732057/22285827432\)	\(4258887944877637632\)	\([2]\)	\(2359296\)	\(2.3235\)
183744.bh1	183744cr4	\([0, 0, 0, -2443116, -1469736016]\)	\(8438952173768857/560166552\)	\(107049495142858752\)	\([2]\)	\(2359296\)	\(2.3235\)