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

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

Rank

The elliptic curves in class 88752bm 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 \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 88752.2.a.bm

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.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 88752bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
88752.bm2	88752bm1	\([0, 1, 0, -21256, 1186292]\)	\(-140246460241/73728\)	\(-558379302912\)	\([]\)	\(314496\)	\(1.2043\)	\(\Gamma_0(N)\)-optimal
88752.bm1	88752bm2	\([0, 1, 0, -1307816, -648904908]\)	\(-32663831300214001/5083731656658\)	\(-38501662036625989632\)	\([]\)	\(4088448\)	\(2.4868\)