Elliptic curve isogeny class with LMFDB label 7752.a (Cremona label 7752g)

• Label: 7752.a
• Number of curves: $4$
• Conductor: $7752$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 7752.a have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(17\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7752.a do not have complex multiplication.

Modular form 7752.2.a.a

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 7752.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7752.a1	7752g4	\([0, -1, 0, -3744, 89244]\)	\(5669532745348/14282091\)	\(14624861184\)	\([4]\)	\(7168\)	\(0.82749\)
7752.a2	7752g3	\([0, -1, 0, -3384, -74340]\)	\(4186423406308/19939113\)	\(20417651712\)	\([2]\)	\(7168\)	\(0.82749\)
7752.a3	7752g2	\([0, -1, 0, -324, 324]\)	\(14738677072/8450649\)	\(2163366144\)	\([2, 2]\)	\(3584\)	\(0.48092\)
7752.a4	7752g1	\([0, -1, 0, 81, 0]\)	\(3628156928/2119203\)	\(-33907248\)	\([2]\)	\(1792\)	\(0.13435\)	\(\Gamma_0(N)\)-optimal