Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-5324.7-d
Conductor 5324.7
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 5324.7-d over \(\Q(\sqrt{-7}) \)

Isogeny class 5324.7-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
5324.7-d1 \( \bigl[1\) , \( -1\) , \( a\) , \( 21 a - 64\) , \( -59 a + 50\bigr] \)
5324.7-d2 \( \bigl[1\) , \( -1\) , \( a\) , \( 39 a + 11\) , \( -46 a - 37\bigr] \)
5324.7-d3 \( \bigl[1\) , \( -1\) , \( a\) , \( 329 a + 211\) , \( -1214 a + 5583\bigr] \)
5324.7-d4 \( \bigl[1\) , \( -1\) , \( a\) , \( 131 a - 614\) , \( 1723 a - 5472\bigr] \)
5324.7-d5 \( \bigl[1\) , \( -1\) , \( a\) , \( 129 a + 23\) , \( 26 a + 989\bigr] \)
5324.7-d6 \( \bigl[1\) , \( -1\) , \( a\) , \( 75 a - 202\) , \( 547 a - 934\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph