Elliptic curve isogeny class with LMFDB label 150.b (Cremona label 150c)

• Label: 150.b
• Number of curves: $8$
• Conductor: $150$
• CM: no
• Rank: $0$

Elliptic curves in class 150.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
150.b1	150c7	\([1, 1, 1, -133338, -18795969]\)	\(16778985534208729/81000\)	\(1265625000\)	\([2]\)	\(576\)	\(1.3689\)
150.b2	150c8	\([1, 1, 1, -11338, -67969]\)	\(10316097499609/5859375000\)	\(91552734375000\)	\([2]\)	\(576\)	\(1.3689\)
150.b3	150c6	\([1, 1, 1, -8338, -295969]\)	\(4102915888729/9000000\)	\(140625000000\)	\([2, 2]\)	\(288\)	\(1.0223\)
150.b4	150c5	\([1, 1, 1, -7213, 232781]\)	\(2656166199049/33750\)	\(527343750\)	\([2]\)	\(192\)	\(0.81958\)
150.b5	150c4	\([1, 1, 1, -1713, -24219]\)	\(35578826569/5314410\)	\(83037656250\)	\([2]\)	\(192\)	\(0.81958\)
150.b6	150c2	\([1, 1, 1, -463, 3281]\)	\(702595369/72900\)	\(1139062500\)	\([2, 2]\)	\(96\)	\(0.47301\)
150.b7	150c3	\([1, 1, 1, -338, -7969]\)	\(-273359449/1536000\)	\(-24000000000\)	\([4]\)	\(144\)	\(0.67574\)
150.b8	150c1	\([1, 1, 1, 37, 281]\)	\(357911/2160\)	\(-33750000\)	\([4]\)	\(48\)	\(0.12643\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 150.b have rank \(0\).

Complex multiplication

The elliptic curves in class 150.b do not have complex multiplication.

Modular form 150.2.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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.