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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-112896.2-c
• Conductor: 112896.2
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
112896.2-c1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 57 a - 339\) , \( -441 a + 2772\bigr] \)
112896.2-c2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -3 a + 21\) , \( -45 a\bigr] \)
112896.2-c3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -63 a + 21\) , \( -201 a + 204\bigr] \)
112896.2-c4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1143 a + 381\) , \( -11865 a + 11652\bigr] \)

Rank

Rank: \( 1 \)

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