Elliptic curve isogeny class with Cremona label 176176bh (LMFDB label 176176.cd)

• Label: 176176bh
• Number of curves: $4$
• Conductor: $176176$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 176176bh have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 5 T + 23 T^{2}\)	1.23.af
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 176176bh do not have complex multiplication.

Modular form 176176.2.a.bh

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 176176bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
176176.cd4	176176bh1	\([0, 0, 0, 1677181, 567482498]\)	\(71903073502287/60782804992\)	\(-441059110069995569152\)	\([2]\)	\(5529600\)	\(2.6490\)	\(\Gamma_0(N)\)-optimal
176176.cd3	176176bh2	\([0, 0, 0, -8235139, 4994324610]\)	\(8511781274893233/3440817243136\)	\(24967649837331477692416\)	\([2, 2]\)	\(11059200\)	\(2.9955\)
176176.cd1	176176bh3	\([0, 0, 0, -114482819, 471315392130]\)	\(22868021811807457713/8953460393696\)	\(64969118713923499851776\)	\([2]\)	\(22118400\)	\(3.3421\)
176176.cd2	176176bh4	\([0, 0, 0, -60584579, -178008847742]\)	\(3389174547561866673/74853681183008\)	\(543161803940867422158848\)	\([2]\)	\(22118400\)	\(3.3421\)