Elliptic curve isogeny class 23409.9-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-23409.9-a
• Conductor: 23409.9
• Rank: \( 1 \)

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

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

Elliptic curves in class 23409.9-a over \(\Q(\sqrt{-2}) \)

Isogeny class 23409.9-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
23409.9-a1	\( \bigl[a\) , \( -1\) , \( 1\) , \( -14 a + 108\) , \( -459 a + 142\bigr] \)
23409.9-a2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 103 a - 98\) , \( 571 a + 120\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph