Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-14700.2-h
Conductor 14700.2
Rank not recorded

Related objects

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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 not yet determined.

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