Elliptic curve isogeny class 32400.2-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-32400.2-d
• Conductor: 32400.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 32400.2-d over \(\Q(\sqrt{-2}) \)

Isogeny class 32400.2-d contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
32400.2-d1	\( \bigl[a\) , \( a\) , \( 0\) , \( -1162 a + 2786\) , \( -17376 a - 34782\bigr] \)
32400.2-d2	\( \bigl[a\) , \( a\) , \( 0\) , \( 38 a - 514\) , \( 504 a - 4302\bigr] \)
32400.2-d3	\( \bigl[a\) , \( a\) , \( 0\) , \( 38 a + 26\) , \( -16 a - 206\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph