Elliptic curve isogeny class with LMFDB label 7440.f (Cremona label 7440c)

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

Rank

The elliptic curves in class 7440.f have rank \(2\).

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.e
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 7440.2.a.f

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.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7440.f1	7440c2	\([0, -1, 0, -5240, 147600]\)	\(7770885300722/9730125\)	\(19927296000\)	\([2]\)	\(13824\)	\(0.88516\)
7440.f2	7440c1	\([0, -1, 0, -240, 3600]\)	\(-1499221444/4359375\)	\(-4464000000\)	\([2]\)	\(6912\)	\(0.53859\)	\(\Gamma_0(N)\)-optimal