Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-252.2-a
Conductor 252.2
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 252.2-a over \(\Q(\sqrt{-7}) \)

Isogeny class 252.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
252.2-a1 \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -3 a - 9\) , \( 5 a + 5\bigr] \)
252.2-a2 \( \bigl[1\) , \( a\) , \( a\) , \( 2 a - 11\) , \( -6 a + 11\bigr] \)
252.2-a3 \( \bigl[1\) , \( 1\) , \( 1\) , \( -4\) , \( 5\bigr] \)
252.2-a4 \( \bigl[1\) , \( 1\) , \( 1\) , \( 386\) , \( 1277\bigr] \)
252.2-a5 \( \bigl[1\) , \( 1\) , \( 1\) , \( -104\) , \( 101\bigr] \)
252.2-a6 \( \bigl[1\) , \( 1\) , \( 1\) , \( -914\) , \( -10915\bigr] \)
252.2-a7 \( \bigl[1\) , \( 1\) , \( 1\) , \( -84\) , \( 261\bigr] \)
252.2-a8 \( \bigl[1\) , \( 1\) , \( 1\) , \( -1344\) , \( 18405\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph