Elliptic curve isogeny class 75.1-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-75.1-b
• Conductor: 75.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 75.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 75.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
75.1-b1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \)
75.1-b2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 225 a - 391\) , \( -392504 a + 679835\bigr] \)
75.1-b3	\( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)
75.1-b4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \)
75.1-b5	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 281 a - 486\) , \( -3516 a + 6090\bigr] \)
75.1-b6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \)
75.1-b7	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 4481 a - 7761\) , \( -217866 a + 377355\bigr] \)
75.1-b8	\( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph