Elliptic curve isogeny class 26244.5-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-26244.5-d
• Conductor: 26244.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 26244.5-d over \(\Q(\sqrt{-2}) \)

Isogeny class 26244.5-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
26244.5-d1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -3 a - 3\) , \( -2 a\bigr] \)
26244.5-d2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 27 a - 33\) , \( -108 a + 64\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph