Elliptic curve isogeny class 61731.3-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-61731.3-b
• Conductor: 61731.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 61731.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 61731.3-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
61731.3-b1	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -9143 a + 10240\) , \( 68164 a + 329450\bigr] \)
61731.3-b2	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -128 a + 535\) , \( -4787 a + 13769\bigr] \)
61731.3-b3	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 22 a - 95\) , \( 103 a - 271\bigr] \)
61731.3-b4	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 97 a - 410\) , \( -980 a + 2978\bigr] \)
61731.3-b5	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 5287 a + 5950\) , \( -322106 a + 404732\bigr] \)
61731.3-b6	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 1522 a - 6395\) , \( -66245 a + 194783\bigr] \)

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