Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-5202.5-d
Conductor 5202.5
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 5202.5-d over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.5-d contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
5202.5-d1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -8560 a + 22289\) , \( -811360 a - 1058718\bigr] \)
5202.5-d2 \( \bigl[1\) , \( 0\) , \( 1\) , \( 8560 a + 22289\) , \( 811360 a - 1058718\bigr] \)
5202.5-d3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1090 a + 104\) , \( -12160 a + 18366\bigr] \)
5202.5-d4 \( \bigl[1\) , \( 0\) , \( 1\) , \( 1090 a + 104\) , \( 12160 a + 18366\bigr] \)
5202.5-d5 \( \bigl[1\) , \( 0\) , \( 1\) , \( -216\) , \( 2062\bigr] \)
5202.5-d6 \( \bigl[1\) , \( 0\) , \( 1\) , \( 1809\) , \( -37790\bigr] \)
5202.5-d7 \( \bigl[1\) , \( 0\) , \( 1\) , \( -751\) , \( -6046\bigr] \)
5202.5-d8 \( \bigl[1\) , \( 0\) , \( 1\) , \( -256\) , \( 1550\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph