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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-150.1-d
• 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-d over \(\Q(\sqrt{6}) \)

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

Curve label	Weierstrass Coefficients
150.1-d1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 291 a + 645\) , \( 5778 a + 14337\bigr] \)
150.1-d2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -119 a - 295\) , \( 720 a + 1765\bigr] \)
150.1-d3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -39 a - 95\) , \( -256 a - 627\bigr] \)
150.1-d4	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -1809 a - 4435\) , \( 63246 a + 154921\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph