Elliptic curve isogeny class with Cremona label 7744bb (LMFDB label 7744.bf)

• Label: 7744bb
• Number of curves: $2$
• Conductor: $7744$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 7744bb have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

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

Modular form 7744.2.a.bb

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 7744bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7744.bf2	7744bb1	\([0, -1, 0, -161, 3137]\)	\(-121\)	\(-3838050304\)	\([]\)	\(3072\)	\(0.52176\)	\(\Gamma_0(N)\)-optimal
7744.bf1	7744bb2	\([0, -1, 0, -232481, -43068991]\)	\(-24729001\)	\(-56192894500864\)	\([]\)	\(33792\)	\(1.7207\)