Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-135.3-a
Conductor 135.3
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 135.3-a over \(\Q(\sqrt{-11}) \)

Isogeny class 135.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
135.3-a1 \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -7 a - 2\) , \( 6 a + 2\bigr] \)
135.3-a2 \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -2 a - 2\) , \( 2\bigr] \)
135.3-a3 \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 23 a + 13\) , \( 40 a - 128\bigr] \)
135.3-a4 \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 13 a - 2\) , \( 10 a + 16\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph