Elliptic curve isogeny class 98.1-a over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-98.1-a
• Conductor: 98.1
• Rank: \( 0 \)

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