Elliptic curve isogeny class 136900.2-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-136900.2-e
• Conductor: 136900.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 136900.2-e over \(\Q(\sqrt{-3}) \)

Isogeny class 136900.2-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
136900.2-e1	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 25 a - 25\) , \( -209\bigr] \)
136900.2-e2	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -5 a + 5\) , \( 5\bigr] \)
136900.2-e3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -25 a + 25\) , \( -39\bigr] \)
136900.2-e4	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -395 a + 395\) , \( -2925\bigr] \)

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