Elliptic curve isogeny class 14700.2-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-14700.2-d
• Conductor: 14700.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 14700.2-d over \(\Q(\sqrt{-3}) \)

Isogeny class 14700.2-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
14700.2-d1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -980\) , \( -15325\bigr] \)
14700.2-d2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 10\) , \( -13\bigr] \)
14700.2-d3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -70\) , \( -205\bigr] \)
14700.2-d4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -370\) , \( 2435\bigr] \)
14700.2-d5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -1050\) , \( -13533\bigr] \)
14700.2-d6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -16800\) , \( -845133\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph