Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-99.3-a
Conductor 99.3
Rank \( 0 \)

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

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

Elliptic curves in class 99.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 99.3-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
99.3-a1 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -12 a - 90\) , \( 71 a + 302\bigr] \)
99.3-a2 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 3 a + 95\) , \( 251 a - 30\bigr] \)
99.3-a3 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a - 5\) , \( a + 4\bigr] \)
99.3-a4 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \)
99.3-a5 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 8 a\) , \( 19 a + 22\bigr] \)
99.3-a6 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 173 a - 15\) , \( 859 a + 1006\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph