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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-288.1-q
• 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-q over \(\Q(\sqrt{10}) \)

Isogeny class 288.1-q contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
288.1-q1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( -8\bigr] \)
288.1-q2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -2\) , \( 0\bigr] \)
288.1-q3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -17\) , \( 33\bigr] \)
288.1-q4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -32\) , \( -60\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph