Elliptic curve isogeny class with Cremona label 76608fu (LMFDB label 76608.bw)

• Label: 76608fu
• Number of curves: $4$
• Conductor: $76608$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 76608fu 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
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 76608.2.a.fu

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 76608fu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
76608.bw4	76608fu1	\([0, 0, 0, -156936, -9372904]\)	\(572616640141312/280535480757\)	\(209418614243177472\)	\([2]\)	\(786432\)	\(2.0169\)	\(\Gamma_0(N)\)-optimal
76608.bw2	76608fu2	\([0, 0, 0, -1337916, 589147760]\)	\(22174957026242512/278654127129\)	\(3328227060564639744\)	\([2, 2]\)	\(1572864\)	\(2.3635\)
76608.bw3	76608fu3	\([0, 0, 0, -229836, 1535448080]\)	\(-28104147578308/21301741002339\)	\(-1017706524882051465216\)	\([2]\)	\(3145728\)	\(2.7100\)
76608.bw1	76608fu4	\([0, 0, 0, -21341676, 37948169936]\)	\(22501000029889239268/3620708343\)	\(172982034893832192\)	\([2]\)	\(3145728\)	\(2.7100\)