Elliptic curve isogeny class 112896.2-i over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-112896.2-i
• Conductor: 112896.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 112896.2-i over \(\Q(\sqrt{-3}) \)

Isogeny class 112896.2-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
112896.2-i1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -503 a + 193\) , \( -3157 a + 3444\bigr] \)
112896.2-i2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2663 a + 3493\) , \( -28801 a - 52668\bigr] \)
112896.2-i3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 1657 a - 2027\) , \( -29617 a + 35172\bigr] \)
112896.2-i4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -503 a + 253\) , \( -3961 a + 3060\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph