Elliptic curve isogeny class with Cremona label 87616l (LMFDB label 87616.bm)

• Label: 87616l
• Number of curves: $2$
• Conductor: $87616$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 87616l have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 6 T + 23 T^{2}\)	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 87616l do not have complex multiplication.

Modular form 87616.2.a.l

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 87616l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
87616.bm1	87616l1	\([0, -1, 0, -4119777, 3241034081]\)	\(-8398297/64\)	\(-58929626493994663936\)	\([]\)	\(4091904\)	\(2.6235\)	\(\Gamma_0(N)\)-optimal
87616.bm2	87616l2	\([0, -1, 0, 12089183, 17229366561]\)	\(212207543/262144\)	\(-241375750119402143481856\)	\([]\)	\(12275712\)	\(3.1728\)