Elliptic curve isogeny class 150.1-f over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-150.1-f
• Conductor: 150.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 150.1-f over \(\Q(\sqrt{6}) \)

Isogeny class 150.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
150.1-f1	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 39 a - 95\) , \( 256 a - 627\bigr] \)
150.1-f2	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 1809 a - 4435\) , \( -63246 a + 154921\bigr] \)
150.1-f3	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 119 a - 295\) , \( -720 a + 1765\bigr] \)
150.1-f4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -291 a + 645\) , \( -5778 a + 14337\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph