Elliptic curve isogeny class 27648.3-z over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27648.3-z
• Conductor: 27648.3
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 27648.3-z over \(\Q(\sqrt{-2}) \)

Isogeny class 27648.3-z contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
27648.3-z1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 62 a + 319\) , \( -1423 a + 769\bigr] \)
27648.3-z2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 190 a - 193\) , \( 1497 a - 399\bigr] \)
27648.3-z3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -58 a + 79\) , \( 161 a + 481\bigr] \)
27648.3-z4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -10 a - 113\) , \( 41 a + 529\bigr] \)
27648.3-z5	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 10 a - 13\) , \( 21 a - 3\bigr] \)
27648.3-z6	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 2 a + 19\) , \( -19 a + 13\bigr] \)