Elliptic curve isogeny class 169.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-169.1-b
• Conductor: 169.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 169.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 169.1-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
169.1-b1	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 957 a - 1656\) , \( 20670 a - 35801\bigr] \)
169.1-b2	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 11 a - 21\) , \( -27 a + 46\bigr] \)
169.1-b3	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 16 a - 46\) , \( 16 a - 66\bigr] \)
169.1-b4	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 42 a - 71\) , \( -182 a + 316\bigr] \)
169.1-b5	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 77462 a - 134191\) , \( 15405299 a - 26682837\bigr] \)
169.1-b6	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 991 a - 3101\) , \( 31242 a - 74777\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 6 & 2 & 3 & 3 & 6 \\ 6 & 1 & 3 & 2 & 18 & 9 \\ 2 & 3 & 1 & 6 & 6 & 3 \\ 3 & 2 & 6 & 1 & 9 & 18 \\ 3 & 18 & 6 & 9 & 1 & 2 \\ 6 & 9 & 3 & 18 & 2 & 1 \end{array}\right)\)

Isogeny graph