Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-14400.5-d
Conductor 14400.5
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 14400.5-d over \(\Q(\sqrt{-11}) \)

Isogeny class 14400.5-d contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
14400.5-d1 \( \bigl[0\) , \( -1\) , \( 0\) , \( 23265 a - 9160\) , \( -1129995 a - 1693388\bigr] \)
14400.5-d2 \( \bigl[0\) , \( -1\) , \( 0\) , \( -35 a - 60\) , \( -735 a - 1908\bigr] \)
14400.5-d3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -65 a - 295\) , \( -25 a + 625\bigr] \)
14400.5-d4 \( \bigl[0\) , \( -1\) , \( 0\) , \( 3665 a + 40\) , \( 10725 a + 137172\bigr] \)
14400.5-d5 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1465 a - 560\) , \( -18035 a - 25308\bigr] \)
14400.5-d6 \( \bigl[0\) , \( -1\) , \( 0\) , \( -1295 a + 2280\) , \( -5019 a - 50652\bigr] \)
14400.5-d7 \( \bigl[0\) , \( -1\) , \( 0\) , \( -50 a - 175\) , \( -394 a - 752\bigr] \)
14400.5-d8 \( \bigl[0\) , \( -1\) , \( 0\) , \( -800 a - 2800\) , \( -26044 a - 51152\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 16 & 4 & 2 & 8 & 8 & 16 \\ 4 & 1 & 4 & 4 & 2 & 2 & 2 & 4 \\ 16 & 4 & 1 & 16 & 8 & 8 & 2 & 4 \\ 4 & 4 & 16 & 1 & 2 & 8 & 8 & 16 \\ 2 & 2 & 8 & 2 & 1 & 4 & 4 & 8 \\ 8 & 2 & 8 & 8 & 4 & 1 & 4 & 8 \\ 8 & 2 & 2 & 8 & 4 & 4 & 1 & 2 \\ 16 & 4 & 4 & 16 & 8 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph