Elliptic curve isogeny class 288.1-a over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-288.1-a
• Conductor: 288.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 288.1-a over \(\Q(\sqrt{10}) \)

Isogeny class 288.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
288.1-a1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 676 a - 2141\) , \( 17735 a - 56086\bigr] \)
288.1-a2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 16 a - 46\) , \( -426 a + 1344\bigr] \)
288.1-a3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 36 a - 111\) , \( -171 a + 540\bigr] \)
288.1-a4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 576 a - 1821\) , \( -12789 a + 40446\bigr] \)
288.1-a5	\( \bigl[0\) , \( -a\) , \( 0\) , \( 56 a - 181\) , \( 123 a - 390\bigr] \)
288.1-a6	\( \bigl[0\) , \( -a\) , \( 0\) , \( -244 a + 659\) , \( 207 a - 1014\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph