Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-12996.2-c
Conductor 12996.2
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 12996.2-c over \(\Q(\sqrt{-11}) \)

Isogeny class 12996.2-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
12996.2-c1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -418\) , \( -3610\bigr] \)
12996.2-c2 \( \bigl[1\) , \( 0\) , \( 0\) , \( 32\) , \( 8\bigr] \)
12996.2-c3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -8\) , \( 0\bigr] \)
12996.2-c4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -428\) , \( -3444\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph