Elliptic curve isogeny class 23409.8-f over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-23409.8-f
• Conductor: 23409.8
• Rank: \( 0 \)

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

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

Elliptic curves in class 23409.8-f over \(\Q(\sqrt{-2}) \)

Isogeny class 23409.8-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
23409.8-f1	\( \bigl[a\) , \( -1\) , \( 1\) , \( 67 a + 75\) , \( 189 a - 1077\bigr] \)
23409.8-f2	\( \bigl[a\) , \( -1\) , \( 1\) , \( -8 a + 9\) , \( 12 a + 34\bigr] \)
23409.8-f3	\( \bigl[a\) , \( -1\) , \( 1\) , \( -38 a + 45\) , \( -21 a - 236\bigr] \)
23409.8-f4	\( \bigl[a\) , \( -1\) , \( 1\) , \( 337 a + 399\) , \( -1242 a + 5565\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 3 & 2 \\ 6 & 1 & 2 & 3 \\ 3 & 2 & 1 & 6 \\ 2 & 3 & 6 & 1 \end{array}\right)\)

Isogeny graph