Elliptic curve isogeny class 12337.6-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-12337.6-a
• Conductor: 12337.6
• Rank: \( 1 \)

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

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

Elliptic curves in class 12337.6-a over \(\Q(\sqrt{-3}) \)

Isogeny class 12337.6-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
12337.6-a1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -143 a + 186\) , \( 388 a + 598\bigr] \)
12337.6-a2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 77 a - 44\) , \( 178 a + 34\bigr] \)
12337.6-a3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -183 a + 151\) , \( 1159 a + 153\bigr] \)
12337.6-a4	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 2 a - 4\) , \( 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph