Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-14400.6-b
Conductor 14400.6
Rank \( 1 \)

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 14400.6-b over \(\Q(\sqrt{-11}) \)

Isogeny class 14400.6-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
14400.6-b1 \( \bigl[0\) , \( -1\) , \( 0\) , \( -312 a + 1296\) , \( 8388 a + 5616\bigr] \)
14400.6-b2 \( \bigl[0\) , \( -1\) , \( 0\) , \( -707 a + 636\) , \( 4329 a - 16956\bigr] \)
14400.6-b3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -727 a - 24\) , \( -4475 a - 23988\bigr] \)
14400.6-b4 \( \bigl[0\) , \( -1\) , \( 0\) , \( -42 a + 81\) , \( 234 a - 216\bigr] \)
14400.6-b5 \( \bigl[0\) , \( -1\) , \( 0\) , \( 263 a - 479\) , \( 2055 a - 1623\bigr] \)
14400.6-b6 \( \bigl[0\) , \( -1\) , \( 0\) , \( -11327 a + 10176\) , \( 264573 a - 1072404\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph