Elliptic curve isogeny class 112896.3-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-112896.3-e
• Conductor: 112896.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 112896.3-e over \(\Q(\sqrt{-3}) \)

Isogeny class 112896.3-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
112896.3-e1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -18\) , \( 17 a - 3\bigr] \)
112896.3-e2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 85 a - 203\) , \( 621 a - 1136\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph