Elliptic curve isogeny class with Cremona label 7744f (LMFDB label 7744.x)

• Label: 7744f
• Number of curves: $3$
• Conductor: $7744$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 7744f have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7744f do not have complex multiplication.

Modular form 7744.2.a.f

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 7744f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7744.x3	7744f1	\([0, 1, 0, -161, -1927]\)	\(-4096/11\)	\(-1247178944\)	\([]\)	\(1920\)	\(0.43279\)	\(\Gamma_0(N)\)-optimal
7744.x2	7744f2	\([0, 1, 0, -5001, 244913]\)	\(-122023936/161051\)	\(-18259946919104\)	\([]\)	\(9600\)	\(1.2375\)
7744.x1	7744f3	\([0, 1, 0, -3785041, 2833092073]\)	\(-52893159101157376/11\)	\(-1247178944\)	\([]\)	\(48000\)	\(2.0422\)