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

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

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	\([1, 0, 1, 105, -191]\)	\(129784785047/92307627\)	\(-92307627\)	\([2]\)	\(30\)	\(0.21683\)

Rank

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

Complex multiplication

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

Modular form 129.2.a.b

Isogeny matrix

The \(i,j\) 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.