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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-61731.2-c
• 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-c over \(\Q(\sqrt{-3}) \)

Isogeny class 61731.2-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
61731.2-c1	\( \bigl[1\) , \( -1\) , \( a\) , \( 601 a - 417\) , \( 4772 a - 273\bigr] \)
61731.2-c2	\( \bigl[1\) , \( a\) , \( 0\) , \( -a - 145\) , \( -222 a - 909\bigr] \)
61731.2-c3	\( \bigl[1\) , \( a\) , \( 0\) , \( -56 a + 40\) , \( 81 a - 156\bigr] \)
61731.2-c4	\( \bigl[1\) , \( -1\) , \( a\) , \( 46 a - 27\) , \( 44 a - 24\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph