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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-61731.3-c
• 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-c over \(\Q(\sqrt{-3}) \)

Isogeny class 61731.3-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
61731.3-c1	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -16 a - 40\) , \( -81 a - 75\bigr] \)
61731.3-c2	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -146 a + 145\) , \( 222 a - 1131\bigr] \)
61731.3-c3	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 18 a + 27\) , \( -45 a + 20\bigr] \)
61731.3-c4	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 183 a + 417\) , \( -4773 a + 4499\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph