Elliptic curve isogeny class with Cremona label 76608ft (LMFDB label 76608.bo)

• Label: 76608ft
• Number of curves: $2$
• Conductor: $76608$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 76608ft have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 76608ft do not have complex multiplication.

Modular form 76608.2.a.ft

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 76608ft

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
76608.bo1	76608ft1	\([0, 0, 0, -203916, -28274416]\)	\(4906933498657/1032471552\)	\(197308386222538752\)	\([2]\)	\(737280\)	\(2.0334\)	\(\Gamma_0(N)\)-optimal
76608.bo2	76608ft2	\([0, 0, 0, 441204, -170974960]\)	\(49702082429663/94844496096\)	\(-18125065461165981696\)	\([2]\)	\(1474560\)	\(2.3799\)