Elliptic curve isogeny class with LMFDB label 76176.bz (Cremona label 76176ca)

• Label: 76176.bz
• Number of curves: $4$
• Conductor: $76176$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 76176.bz have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 76176.bz do not have complex multiplication.

Modular form 76176.2.a.bz

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 76176.bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
76176.bz1	76176ca4	\([0, 0, 0, -18817059, -31412882270]\)	\(1666957239793/301806\)	\(133408150023472275456\)	\([2]\)	\(3244032\)	\(2.8652\)
76176.bz2	76176ca3	\([0, 0, 0, -8152419, 8666967778]\)	\(135559106353/5037138\)	\(2226580193875976921088\)	\([2]\)	\(3244032\)	\(2.8652\)
76176.bz3	76176ca2	\([0, 0, 0, -1296579, -384112190]\)	\(545338513/171396\)	\(75762653099749687296\)	\([2, 2]\)	\(1622016\)	\(2.5186\)
76176.bz4	76176ca1	\([0, 0, 0, 226941, -40710782]\)	\(2924207/3312\)	\(-1464012620285018112\)	\([2]\)	\(811008\)	\(2.1721\)	\(\Gamma_0(N)\)-optimal