Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-2178.5-c
Conductor 2178.5
Rank \( 0 \)

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 2178.5-c over \(\Q(\sqrt{-2}) \)

Isogeny class 2178.5-c contains 8 curves linked by isogenies of degrees dividing 20.

Curve label Weierstrass Coefficients
2178.5-c1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -10055\) , \( -390309\bigr] \)
2178.5-c2 \( \bigl[1\) , \( 0\) , \( 0\) , \( -500 a + 1395\) , \( 12836 a + 15601\bigr] \)
2178.5-c3 \( \bigl[1\) , \( 0\) , \( 0\) , \( 500 a + 1395\) , \( -12836 a + 15601\bigr] \)
2178.5-c4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -3475 a - 9975\) , \( 281251 a - 416249\bigr] \)
2178.5-c5 \( \bigl[1\) , \( 0\) , \( 0\) , \( 3475 a - 9975\) , \( -281251 a - 416249\bigr] \)
2178.5-c6 \( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \)
2178.5-c7 \( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \)
2178.5-c8 \( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 10 & 10 & 2 & 2 & 5 & 10 & 2 \\ 10 & 1 & 4 & 20 & 5 & 2 & 4 & 20 \\ 10 & 4 & 1 & 5 & 20 & 2 & 4 & 20 \\ 2 & 20 & 5 & 1 & 4 & 10 & 20 & 4 \\ 2 & 5 & 20 & 4 & 1 & 10 & 20 & 4 \\ 5 & 2 & 2 & 10 & 10 & 1 & 2 & 10 \\ 10 & 4 & 4 & 20 & 20 & 2 & 1 & 5 \\ 2 & 20 & 20 & 4 & 4 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph