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

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

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

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

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

Isogeny class 32400.3-c contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
32400.3-c1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -3960\) , \( 182120\bigr] \)
32400.3-c2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 0\) , \( -40\bigr] \)
32400.3-c3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 1260\) , \( 8528\bigr] \)
32400.3-c4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -360\) , \( 1400\bigr] \)
32400.3-c5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -180\) , \( -832\bigr] \)
32400.3-c6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -4860\) , \( 132800\bigr] \)
32400.3-c7	\( \bigl[a\) , \( -1\) , \( 0\) , \( -2880\) , \( -58072\bigr] \)
32400.3-c8	\( \bigl[a\) , \( -1\) , \( 0\) , \( -77760\) , \( 8385080\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph