Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-39600.5-h
Conductor 39600.5
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 39600.5-h over \(\Q(\sqrt{-11}) \)

Isogeny class 39600.5-h contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
39600.5-h1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -15621\) , \( -757296\bigr] \)
39600.5-h2 \( \bigl[0\) , \( 1\) , \( 0\) , \( -2035 a + 4564\) , \( -34353 a - 101124\bigr] \)
39600.5-h3 \( \bigl[0\) , \( 1\) , \( 0\) , \( 219\) , \( -4500\bigr] \)
39600.5-h4 \( \bigl[0\) , \( 1\) , \( 0\) , \( 2165 a - 16676\) , \( -217977 a - 659412\bigr] \)
39600.5-h5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -2165 a - 14511\) , \( 217977 a - 877389\bigr] \)
39600.5-h6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -3156\) , \( -63900\bigr] \)
39600.5-h7 \( \bigl[0\) , \( 1\) , \( 0\) , \( 2035 a + 2529\) , \( 34353 a - 135477\bigr] \)
39600.5-h8 \( \bigl[0\) , \( 1\) , \( 0\) , \( -249996\) , \( -48194796\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph