Elliptic curve isogeny class 29241.9-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-29241.9-b
• Conductor: 29241.9
• Rank: \( 0 \)

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

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

Elliptic curves in class 29241.9-b over \(\Q(\sqrt{-2}) \)

Isogeny class 29241.9-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
29241.9-b1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 1641 a + 3000\) , \( -38959 a + 86997\bigr] \)
29241.9-b2	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -114 a - 150\) , \( 938 a + 489\bigr] \)
29241.9-b3	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -384 a + 615\) , \( 3710 a + 11046\bigr] \)
29241.9-b4	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -6729 a + 10470\) , \( 208667 a + 588603\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph