Elliptic curve isogeny class 61731.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-61731.2-b
• Conductor: 61731.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 61731.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 61731.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
61731.2-b1	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 11237 a - 5950\) , \( 322105 a + 82626\bigr] \)
61731.2-b2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 407 a - 535\) , \( 4786 a + 8982\bigr] \)
61731.2-b3	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -73 a + 95\) , \( -104 a - 168\bigr] \)
61731.2-b4	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -313 a + 410\) , \( 979 a + 1998\bigr] \)
61731.2-b5	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 1097 a - 10240\) , \( -68165 a + 397614\bigr] \)
61731.2-b6	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -4873 a + 6395\) , \( 66244 a + 128538\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph