Elliptic curve isogeny class with Cremona label 7752e (LMFDB label 7752.b)

• Label: 7752e
• Number of curves: $2$
• Conductor: $7752$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 7752e have rank \(2\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 7752.2.a.e

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 Cremona numbering.

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

Isogeny graph

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

Elliptic curves in class 7752e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7752.b2	7752e1	\([0, -1, 0, -484, 4228]\)	\(49081386832/497097\)	\(127256832\)	\([2]\)	\(2560\)	\(0.37309\)	\(\Gamma_0(N)\)-optimal
7752.b1	7752e2	\([0, -1, 0, -864, -2916]\)	\(69737687428/36026451\)	\(36891085824\)	\([2]\)	\(5120\)	\(0.71966\)