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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-14700.2-h
• Conductor: 14700.2
• Rank: \( 0 \)

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

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

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

Isogeny class 14700.2-h contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
14700.2-h1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 81 a\) , \( 6561\bigr] \)
14700.2-h2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -729 a\) , \( -176985\bigr] \)
14700.2-h3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 41 a\) , \( -39\bigr] \)
14700.2-h4	\( \bigl[a\) , \( 0\) , \( 0\) , \( 6451 a\) , \( 124931\bigr] \)
14700.2-h5	\( \bigl[a\) , \( 0\) , \( 0\) , \( 2701 a\) , \( -52819\bigr] \)
14700.2-h6	\( \bigl[a\) , \( 0\) , \( 0\) , \( 361 a\) , \( 2585\bigr] \)
14700.2-h7	\( \bigl[a\) , \( 0\) , \( 0\) , \( 2681 a\) , \( -53655\bigr] \)
14700.2-h8	\( \bigl[a\) , \( 0\) , \( 0\) , \( 5761 a\) , \( 167825\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph