Elliptic curve isogeny class with LMFDB label 129.b (Cremona label 129b)

• Label: 129.b
• Number of curves: $4$
• Conductor: $129$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 129.b have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(43\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(5\)	\( 1 - 2 T + 5 T^{2}\)	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
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 129.b do not have complex multiplication.

Modular form 129.2.a.b

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 129.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
129.b1	129b3	\([1, 0, 1, -245, 1433]\)	\(1616855892553/22851963\)	\(22851963\)	\([4]\)	\(30\)	\(0.21683\)
129.b2	129b1	\([1, 0, 1, -30, -29]\)	\(2845178713/1347921\)	\(1347921\)	\([2, 2]\)	\(15\)	\(-0.12975\)	\(\Gamma_0(N)\)-optimal
129.b3	129b2	\([1, 0, 1, -25, -49]\)	\(1630532233/1161\)	\(1161\)	\([2]\)	\(30\)	\(-0.47632\)
129.b4	129b4	\([1, 0, 1, 105, -191]\)	\(129784785047/92307627\)	\(-92307627\)	\([2]\)	\(30\)	\(0.21683\)