Elliptic curve isogeny class 27648.4-l over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-27648.4-l
• Conductor: 27648.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 27648.4-l over \(\Q(\sqrt{-2}) \)

Isogeny class 27648.4-l contains 4 curves linked by isogenies of degrees dividing 27.

Curve label	Weierstrass Coefficients
27648.4-l1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -50 a - 49\) , \( -239 a - 15\bigr] \)
27648.4-l2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -10 a - 65\) , \( 33 a + 49\bigr] \)
27648.4-l3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -314 a + 959\) , \( 7569 a + 8177\bigr] \)
27648.4-l4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 6 a + 159\) , \( -495 a + 17\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 9 & 3 \\ 3 & 1 & 27 & 9 \\ 9 & 27 & 1 & 3 \\ 3 & 9 & 3 & 1 \end{array}\right)\)

Isogeny graph