Elliptic curve isogeny class with LMFDB label 7440.bb (Cremona label 7440z)

• Label: 7440.bb
• Number of curves: $2$
• Conductor: $7440$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 7440.bb have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(31\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7440.bb do not have complex multiplication.

Modular form 7440.2.a.bb

Isogeny matrix

The \((i,j)\)-th entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 7440.bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7440.bb1	7440z2	\([0, 1, 0, -760, -7852]\)	\(11867954041/778410\)	\(3188367360\)	\([2]\)	\(4608\)	\(0.57329\)
7440.bb2	7440z1	\([0, 1, 0, 40, -492]\)	\(1685159/27900\)	\(-114278400\)	\([2]\)	\(2304\)	\(0.22672\)	\(\Gamma_0(N)\)-optimal