Elliptic curve isogeny class with Cremona label 9680t (LMFDB label 9680.ba)

• Label: 9680t
• Number of curves: $4$
• Conductor: $9680$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 9680t have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9680t do not have complex multiplication.

Modular form 9680.2.a.t

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 9680t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9680.ba3	9680t1	\([0, -1, 0, -161, 596]\)	\(16384/5\)	\(141724880\)	\([2]\)	\(2880\)	\(0.26900\)	\(\Gamma_0(N)\)-optimal
9680.ba4	9680t2	\([0, -1, 0, 444, 3500]\)	\(21296/25\)	\(-11337990400\)	\([2]\)	\(5760\)	\(0.61557\)
9680.ba1	9680t3	\([0, -1, 0, -5001, -134440]\)	\(488095744/125\)	\(3543122000\)	\([2]\)	\(8640\)	\(0.81830\)
9680.ba2	9680t4	\([0, -1, 0, -4396, -168804]\)	\(-20720464/15625\)	\(-7086244000000\)	\([2]\)	\(17280\)	\(1.1649\)