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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-112896.2-b
• 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-b over \(\Q(\sqrt{-3}) \)

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

Curve label	Weierstrass Coefficients
112896.2-b1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -310 a - 193\) , \( 3157 a + 287\bigr] \)
112896.2-b2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 830 a - 3493\) , \( 28801 a - 81469\bigr] \)
112896.2-b3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -250 a - 253\) , \( 3961 a - 901\bigr] \)
112896.2-b4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -370 a + 2027\) , \( 29617 a + 5555\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph