Elliptic curve isogeny class 6498.5-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-6498.5-c
• Conductor: 6498.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 6498.5-c over \(\Q(\sqrt{-2}) \)

Isogeny class 6498.5-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
6498.5-c1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -418\) , \( -3610\bigr] \)
6498.5-c2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 715 a - 338\) , \( -11645 a - 8942\bigr] \)
6498.5-c3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -715 a - 338\) , \( 11645 a - 8942\bigr] \)
6498.5-c4	\( \bigl[1\) , \( 0\) , \( 0\) , \( 32\) , \( 8\bigr] \)
6498.5-c5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -8\) , \( 0\bigr] \)
6498.5-c6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -10 a + 352\) , \( 1790 a + 184\bigr] \)
6498.5-c7	\( \bigl[1\) , \( 0\) , \( 0\) , \( 10 a + 352\) , \( -1790 a + 184\bigr] \)
6498.5-c8	\( \bigl[1\) , \( 0\) , \( 0\) , \( -428\) , \( -3444\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 2 & 3 & 6 & 6 & 6 & 2 \\ 2 & 1 & 4 & 6 & 12 & 12 & 3 & 4 \\ 2 & 4 & 1 & 6 & 12 & 3 & 12 & 4 \\ 3 & 6 & 6 & 1 & 2 & 2 & 2 & 6 \\ 6 & 12 & 12 & 2 & 1 & 4 & 4 & 3 \\ 6 & 12 & 3 & 2 & 4 & 1 & 4 & 12 \\ 6 & 3 & 12 & 2 & 4 & 4 & 1 & 12 \\ 2 & 4 & 4 & 6 & 3 & 12 & 12 & 1 \end{array}\right)\)

Isogeny graph