Elliptic curve isogeny class 343.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-343.2-a
• Conductor: 343.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 343.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 343.2-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
343.2-a1	\( \bigl[1\) , \( a\) , \( a\) , \( 6 a + 48\) , \( 416 a + 152\bigr] \)
343.2-a2	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -44 a + 56\) , \( -540 a + 143\bigr] \)
343.2-a3	\( \bigl[1\) , \( a\) , \( a\) , \( -4 a - 7\) , \( -9 a - 5\bigr] \)
343.2-a4	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 11 a - 9\) , \( 15 a - 14\bigr] \)
343.2-a5	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 51 a - 34\) , \( -79 a - 41\bigr] \)
343.2-a6	\( \bigl[1\) , \( a\) , \( a\) , \( -29 a - 22\) , \( 80 a + 19\bigr] \)
343.2-a7	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 786 a - 524\) , \( -6694 a - 433\bigr] \)
343.2-a8	\( \bigl[1\) , \( a\) , \( a\) , \( -464 a - 332\) , \( 6180 a + 1082\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 12 & 4 & 12 & 6 & 2 & 3 & 4 \\ 12 & 1 & 12 & 4 & 2 & 6 & 4 & 3 \\ 4 & 12 & 1 & 3 & 6 & 2 & 12 & 4 \\ 12 & 4 & 3 & 1 & 2 & 6 & 4 & 12 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 3 & 4 & 12 & 4 & 2 & 6 & 1 & 12 \\ 4 & 3 & 4 & 12 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph