Elliptic curve isogeny class 2601.5-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-2601.5-e
• Conductor: 2601.5
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 2601.5-e over \(\Q(\sqrt{-2}) \)

Isogeny class 2601.5-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2601.5-e1	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -1087 a + 92\) , \( 10290 a - 17475\bigr] \)
2601.5-e2	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -67 a + 7\) , \( 158 a - 254\bigr] \)
2601.5-e3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -7 a - 158\) , \( 2 a - 1661\bigr] \)
2601.5-e4	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -7 a + 12\) , \( 14 a + 23\bigr] \)

Rank

Rank: \( 0 \)

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