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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-75.1-a
• Conductor: 75.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
75.1-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -109\) , \( 770\bigr] \)
75.1-a2	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 227 a - 390\) , \( 392730 a - 680227\bigr] \)
75.1-a3	\( \bigl[a\) , \( 1\) , \( 0\) , \( 36\) , \( 63\bigr] \)
75.1-a4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -9\) , \( 0\bigr] \)
75.1-a5	\( \bigl[1\) , \( -a\) , \( 0\) , \( 281 a - 486\) , \( 3516 a - 6090\bigr] \)
75.1-a6	\( \bigl[a\) , \( 1\) , \( 0\) , \( -134\) , \( 525\bigr] \)
75.1-a7	\( \bigl[1\) , \( -a\) , \( 0\) , \( 4481 a - 7761\) , \( 217866 a - 377355\bigr] \)
75.1-a8	\( \bigl[a\) , \( 1\) , \( 0\) , \( -2159\) , \( 37380\bigr] \)

Rank

Rank: \( 0 \)

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