Elliptic curve isogeny class with LMFDB label 7488.j (Cremona label 7488h)

• Label: 7488.j
• Number of curves: $2$
• Conductor: $7488$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 7488.j have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7488.j do not have complex multiplication.

Modular form 7488.2.a.j

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 7488.j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7488.j1	7488h2	\([0, 0, 0, -36396, -2671056]\)	\(1033364331/676\)	\(3488011517952\)	\([2]\)	\(18432\)	\(1.3464\)
7488.j2	7488h1	\([0, 0, 0, -1836, -58320]\)	\(-132651/208\)	\(-1073234313216\)	\([2]\)	\(9216\)	\(0.99980\)	\(\Gamma_0(N)\)-optimal