Elliptic curve isogeny class with LMFDB label 77616.fq (Cremona label 77616ch)

• Label: 77616.fq
• Number of curves: $4$
• Conductor: $77616$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 77616.fq have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 77616.fq do not have complex multiplication.

Modular form 77616.2.a.fq

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 77616.fq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
77616.fq1	77616ch4	\([0, 0, 0, -208299, -36586438]\)	\(5690357426/891\)	\(156503273084928\)	\([2]\)	\(393216\)	\(1.7347\)
77616.fq2	77616ch2	\([0, 0, 0, -14259, -456190]\)	\(3650692/1089\)	\(95640889107456\)	\([2, 2]\)	\(196608\)	\(1.3881\)
77616.fq3	77616ch1	\([0, 0, 0, -5439, 148862]\)	\(810448/33\)	\(724552190208\)	\([2]\)	\(98304\)	\(1.0415\)	\(\Gamma_0(N)\)-optimal
77616.fq4	77616ch3	\([0, 0, 0, 38661, -3049270]\)	\(36382894/43923\)	\(-7715031721334784\)	\([2]\)	\(393216\)	\(1.7347\)