Elliptic curve isogeny class 90.1-f over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-90.1-f
• Conductor: 90.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Elliptic curves in class 90.1-f over \(\Q(\sqrt{10}) \)

Isogeny class 90.1-f contains 12 curves linked by isogenies of degrees dividing 24.

Curve label	Weierstrass Coefficients
90.1-f1	\( \bigl[1\) , \( 0\) , \( 1\) , \( 12650 a - 45334\) , \( 1494440 a - 4876368\bigr] \)
90.1-f2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -14\) , \( -64\bigr] \)
90.1-f3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 1\) , \( 2\bigr] \)
90.1-f4	\( \bigl[1\) , \( 0\) , \( 1\) , \( 185 a - 469\) , \( 1934 a - 7134\bigr] \)
90.1-f5	\( \bigl[1\) , \( 0\) , \( 1\) , \( -454\) , \( -544\bigr] \)
90.1-f6	\( \bigl[1\) , \( 0\) , \( 1\) , \( -69\) , \( -194\bigr] \)
90.1-f7	\( \bigl[1\) , \( 0\) , \( 1\) , \( -19\) , \( 26\bigr] \)
90.1-f8	\( \bigl[1\) , \( 0\) , \( 1\) , \( -334\) , \( -2368\bigr] \)
90.1-f9	\( \bigl[1\) , \( 0\) , \( 1\) , \( -185 a - 469\) , \( -1934 a - 7134\bigr] \)
90.1-f10	\( \bigl[1\) , \( 0\) , \( 1\) , \( -289\) , \( 1862\bigr] \)
90.1-f11	\( \bigl[1\) , \( 0\) , \( 1\) , \( -5334\) , \( -150368\bigr] \)
90.1-f12	\( \bigl[1\) , \( 0\) , \( 1\) , \( -12650 a - 45334\) , \( -1494440 a - 4876368\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 8 & 24 & 3 & 8 & 6 & 12 & 4 & 12 & 24 & 2 & 4 \\ 8 & 1 & 3 & 24 & 4 & 12 & 6 & 2 & 24 & 12 & 4 & 8 \\ 24 & 3 & 1 & 8 & 12 & 4 & 2 & 6 & 8 & 4 & 12 & 24 \\ 3 & 24 & 8 & 1 & 24 & 2 & 4 & 12 & 4 & 8 & 6 & 12 \\ 8 & 4 & 12 & 24 & 1 & 12 & 6 & 2 & 24 & 3 & 4 & 8 \\ 6 & 12 & 4 & 2 & 12 & 1 & 2 & 6 & 2 & 4 & 3 & 6 \\ 12 & 6 & 2 & 4 & 6 & 2 & 1 & 3 & 4 & 2 & 6 & 12 \\ 4 & 2 & 6 & 12 & 2 & 6 & 3 & 1 & 12 & 6 & 2 & 4 \\ 12 & 24 & 8 & 4 & 24 & 2 & 4 & 12 & 1 & 8 & 6 & 3 \\ 24 & 12 & 4 & 8 & 3 & 4 & 2 & 6 & 8 & 1 & 12 & 24 \\ 2 & 4 & 12 & 6 & 4 & 3 & 6 & 2 & 6 & 12 & 1 & 2 \\ 4 & 8 & 24 & 12 & 8 & 6 & 12 & 4 & 3 & 24 & 2 & 1 \end{array}\right)\)

Isogeny graph