Elliptic curve isogeny class 17856.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-17856.2-a
• Conductor: 17856.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 17856.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 17856.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
17856.2-a1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -319 a - 67\) , \( 2689 a - 748\bigr] \)
17856.2-a2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -19 a - 7\) , \( 25 a - 16\bigr] \)
17856.2-a3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 41 a + 53\) , \( 337 a - 100\bigr] \)
17856.2-a4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 7\) , \( -14 a - 7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph