Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-196.2-a
Conductor 196.2
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 196.2-a over \(\Q(\sqrt{2}) \)

Isogeny class 196.2-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
196.2-a1 \( \bigl[a\) , \( a\) , \( 0\) , \( 6 a - 110\) , \( -2170 a - 2612\bigr] \)
196.2-a2 \( \bigl[a\) , \( a\) , \( 0\) , \( 16 a - 10\) , \( 98 a + 76\bigr] \)
196.2-a3 \( \bigl[a\) , \( a\) , \( 0\) , \( 436 a - 1200\) , \( -10318 a + 15770\bigr] \)
196.2-a4 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -8 a - 7\) , \( -7 a - 8\bigr] \)
196.2-a5 \( \bigl[a\) , \( a\) , \( 0\) , \( -9 a - 15\) , \( 14 a + 20\bigr] \)
196.2-a6 \( \bigl[a\) , \( a\) , \( 0\) , \( -79 a - 225\) , \( -1092 a - 1044\bigr] \)
196.2-a7 \( \bigl[a\) , \( a\) , \( 0\) , \( -154 a - 240\) , \( 1218 a + 1770\bigr] \)
196.2-a8 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 312 a - 479\) , \( -4555 a + 6314\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph