Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-98.1-a
Conductor 98.1
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 98.1-a over \(\Q(\sqrt{2}) \)

Isogeny class 98.1-a contains 12 curves linked by isogenies of degrees dividing 36.

Curve label Weierstrass Coefficients
98.1-a1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)
98.1-a2 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)
98.1-a3 \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \)
98.1-a4 \( \bigl[1\) , \( 0\) , \( 1\) , \( 55 a - 91\) , \( -290 a + 416\bigr] \)
98.1-a5 \( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \)
98.1-a6 \( \bigl[1\) , \( 0\) , \( 1\) , \( 130 a - 356\) , \( 2000 a - 2038\bigr] \)
98.1-a7 \( \bigl[1\) , \( 0\) , \( 1\) , \( 14480 a - 23211\) , \( 1224480 a - 1786730\bigr] \)
98.1-a8 \( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)
98.1-a9 \( \bigl[1\) , \( 0\) , \( 1\) , \( -130 a - 356\) , \( -2000 a - 2038\bigr] \)
98.1-a10 \( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)
98.1-a11 \( \bigl[1\) , \( 0\) , \( 1\) , \( -55 a - 91\) , \( 290 a + 416\bigr] \)
98.1-a12 \( \bigl[1\) , \( 0\) , \( 1\) , \( -14480 a - 23211\) , \( -1224480 a - 1786730\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 9 & 3 & 36 & 6 & 12 & 4 & 18 & 12 & 2 & 36 & 4 \\ 9 & 1 & 3 & 4 & 6 & 12 & 36 & 2 & 12 & 18 & 4 & 36 \\ 3 & 3 & 1 & 12 & 2 & 4 & 12 & 6 & 4 & 6 & 12 & 12 \\ 36 & 4 & 12 & 1 & 6 & 12 & 36 & 2 & 3 & 18 & 4 & 9 \\ 6 & 6 & 2 & 6 & 1 & 2 & 6 & 3 & 2 & 3 & 6 & 6 \\ 12 & 12 & 4 & 12 & 2 & 1 & 3 & 6 & 4 & 6 & 3 & 12 \\ 4 & 36 & 12 & 36 & 6 & 3 & 1 & 18 & 12 & 2 & 9 & 4 \\ 18 & 2 & 6 & 2 & 3 & 6 & 18 & 1 & 6 & 9 & 2 & 18 \\ 12 & 12 & 4 & 3 & 2 & 4 & 12 & 6 & 1 & 6 & 12 & 3 \\ 2 & 18 & 6 & 18 & 3 & 6 & 2 & 9 & 6 & 1 & 18 & 2 \\ 36 & 4 & 12 & 4 & 6 & 3 & 9 & 2 & 12 & 18 & 1 & 36 \\ 4 & 36 & 12 & 9 & 6 & 12 & 4 & 18 & 3 & 2 & 36 & 1 \end{array}\right)\)

Isogeny graph