Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-41616.5-s
Conductor 41616.5
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 41616.5-s over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.5-s contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
41616.5-s1 \( \bigl[a\) , \( 0\) , \( a\) , \( -7106 a - 743\) , \( 216206 a - 243042\bigr] \)
41616.5-s2 \( \bigl[a\) , \( 0\) , \( a\) , \( 34 a + 17\) , \( -38 a - 138\bigr] \)
41616.5-s3 \( \bigl[a\) , \( 0\) , \( a\) , \( 34 a - 63\) , \( 186 a - 442\bigr] \)
41616.5-s4 \( \bigl[a\) , \( 0\) , \( a\) , \( -446 a - 23\) , \( 3626 a - 3426\bigr] \)
41616.5-s5 \( \bigl[a\) , \( 0\) , \( a\) , \( -1466 a + 1337\) , \( 7366 a + 45534\bigr] \)
41616.5-s6 \( \bigl[a\) , \( 0\) , \( a\) , \( 514 a - 1383\) , \( 11082 a - 17554\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph