Elliptic curve isogeny class 32400.3-k over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-32400.3-k
• Conductor: 32400.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 32400.3-k over \(\Q(\sqrt{-2}) \)

Isogeny class 32400.3-k contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
32400.3-k1	\( \bigl[a\) , \( -1\) , \( a\) , \( 51 a + 115\) , \( -887 a - 820\bigr] \)
32400.3-k2	\( \bigl[a\) , \( -1\) , \( a\) , \( -39 a - 65\) , \( -149 a - 100\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph