Elliptic curve isogeny class 27648.2-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27648.2-d
• Conductor: 27648.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 27648.2-d over \(\Q(\sqrt{-2}) \)

Isogeny class 27648.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
27648.2-d1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -24 a - 24\) , \( 58 a + 20\bigr] \)
27648.2-d2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -98 a - 5\) , \( 297 a - 365\bigr] \)
27648.2-d3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -8 a - 5\) , \( -9 a - 5\bigr] \)
27648.2-d4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 42 a + 15\) , \( -23 a - 97\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph