Elliptic curve isogeny class with LMFDB label 7440.r (Cremona label 7440s)

• Label: 7440.r
• Number of curves: $2$
• Conductor: $7440$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 7440.r have rank \(1\).

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

See L-function page for more information

Complex multiplication

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

Modular form 7440.2.a.r

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.r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7440.r1	7440s2	\([0, 1, 0, -2576, -12780]\)	\(461710681489/252204840\)	\(1033031024640\)	\([2]\)	\(9216\)	\(0.99607\)
7440.r2	7440s1	\([0, 1, 0, 624, -1260]\)	\(6549699311/4017600\)	\(-16456089600\)	\([2]\)	\(4608\)	\(0.64950\)	\(\Gamma_0(N)\)-optimal