Elliptic curve isogeny class with Cremona label 87616bb (LMFDB label 87616.bj)

• Label: 87616bb
• Number of curves: $3$
• Conductor: $87616$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 87616bb have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(37\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 87616bb do not have complex multiplication.

Modular form 87616.2.a.bb

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 87616bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
87616.bj3	87616bb1	\([0, 1, 0, -18253, -947855]\)	\(4096000/37\)	\(6075640136512\)	\([]\)	\(131328\)	\(1.2755\)	\(\Gamma_0(N)\)-optimal
87616.bj2	87616bb2	\([0, 1, 0, -127773, 16980569]\)	\(1404928000/50653\)	\(8317551346884928\)	\([]\)	\(393984\)	\(1.8248\)
87616.bj1	87616bb3	\([0, 1, 0, -10258373, 12642949961]\)	\(727057727488000/37\)	\(6075640136512\)	\([]\)	\(1181952\)	\(2.3741\)