Elliptic curve isogeny class 343.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-343.3-a
• Conductor: 343.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 343.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 343.3-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
343.3-a1	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -57 a + 46\) , \( 551 a - 453\bigr] \)
343.3-a2	\( \bigl[a\) , \( a\) , \( a + 1\) , \( -49 a - 6\) , \( -417 a + 568\bigr] \)
343.3-a3	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 8 a - 9\) , \( -14 a + 10\bigr] \)
343.3-a4	\( \bigl[a\) , \( a\) , \( a + 1\) , \( 6 a + 4\) , \( 8 a - 14\bigr] \)
343.3-a5	\( \bigl[a\) , \( a\) , \( a + 1\) , \( 21 a + 29\) , \( -81 a + 99\bigr] \)
343.3-a6	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 33 a - 49\) , \( 95 a - 86\bigr] \)
343.3-a7	\( \bigl[a\) , \( a\) , \( a + 1\) , \( 331 a + 464\) , \( -6181 a + 7262\bigr] \)
343.3-a8	\( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 523 a - 784\) , \( 6955 a - 6603\bigr] \)

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