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

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

Elliptic curves in class 150c

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

Rank

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

Complex multiplication

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

Modular form 150.2.a.c

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.