Elliptic curve isogeny class with Cremona label 88752h (LMFDB label 88752.bd)

• Label: 88752h
• Number of curves: $2$
• Conductor: $88752$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 88752h have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(43\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 88752h do not have complex multiplication.

Modular form 88752.2.a.h

Isogeny matrix

The \(i,j\) 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.

Elliptic curves in class 88752h

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
88752.bd2	88752h1	\([0, 1, 0, -444, 3276]\)	\(476656/27\)	\(549552384\)	\([2]\)	\(54912\)	\(0.43162\)	\(\Gamma_0(N)\)-optimal
88752.bd1	88752h2	\([0, 1, 0, -1304, -14268]\)	\(3014284/729\)	\(59351657472\)	\([2]\)	\(109824\)	\(0.77819\)