Elliptic curve isogeny class with Cremona label 176b (LMFDB label 176.b)

• Label: 176b
• Number of curves: $3$
• Conductor: $176$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 176b have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - T + 23 T^{2}\)	1.23.ab
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 176b do not have complex multiplication.

Modular form 176.2.a.b

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 176b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
176.b3	176b1	\([0, 1, 0, -5, -13]\)	\(-4096/11\)	\(-45056\)	\([]\)	\(8\)	\(-0.41958\)	\(\Gamma_0(N)\)-optimal
176.b2	176b2	\([0, 1, 0, -165, 1427]\)	\(-122023936/161051\)	\(-659664896\)	\([]\)	\(40\)	\(0.38514\)
176.b1	176b3	\([0, 1, 0, -125125, 16994227]\)	\(-52893159101157376/11\)	\(-45056\)	\([]\)	\(200\)	\(1.1899\)