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

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

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

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

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

Isogeny class 27648.3-l contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
27648.3-l1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 24 a - 24\) , \( -58 a + 20\bigr] \)
27648.3-l2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 98 a - 5\) , \( -297 a - 365\bigr] \)
27648.3-l3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 8 a - 5\) , \( 9 a - 5\bigr] \)
27648.3-l4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -42 a + 15\) , \( 23 a - 97\bigr] \)

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