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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-61731.2-a
• Conductor: 61731.2
• Rank: \( 1 \)

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

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

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

Isogeny class 61731.2-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
61731.2-a1	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -36927 a + 48468\) , \( -1388304 a - 2608018\bigr] \)
61731.2-a2	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 19 a + 6700\) , \( -244436 a + 127622\bigr] \)
61731.2-a3	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 4309 a - 7730\) , \( 192094 a - 234274\bigr] \)
61731.2-a4	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 589 a - 140\) , \( -1616 a - 3991\bigr] \)
61731.2-a5	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( 11 a + 32\) , \( 16 a + 4\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 9 & 9 & 3 & 9 \\ 9 & 1 & 9 & 3 & 9 \\ 9 & 9 & 1 & 3 & 9 \\ 3 & 3 & 3 & 1 & 3 \\ 9 & 9 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph