Elliptic curve isogeny class 2025.8-a over number field \(\Q(\sqrt{-11}) \)

• Base field: \(\Q(\sqrt{-11}) \)
• Label: 2.0.11.1-2025.8-a
• Conductor: 2025.8
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 2025.8-a over \(\Q(\sqrt{-11}) \)

Isogeny class 2025.8-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
2025.8-a1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -990\) , \( 22765\bigr] \)
2025.8-a2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \)
2025.8-a3	\( \bigl[1\) , \( -1\) , \( 0\) , \( 315\) , \( 1066\bigr] \)
2025.8-a4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -90\) , \( 175\bigr] \)
2025.8-a5	\( \bigl[1\) , \( -1\) , \( 0\) , \( -45\) , \( -104\bigr] \)
2025.8-a6	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1215\) , \( 16600\bigr] \)
2025.8-a7	\( \bigl[1\) , \( -1\) , \( 0\) , \( -720\) , \( -7259\bigr] \)
2025.8-a8	\( \bigl[1\) , \( -1\) , \( 0\) , \( -19440\) , \( 1048135\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph