Elliptic curve isogeny class 6084.2-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-6084.2-e
• Conductor: 6084.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 6084.2-e over \(\Q(\sqrt{-2}) \)

Isogeny class 6084.2-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
6084.2-e1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -13\) , \( -4\bigr] \)
6084.2-e2	\( \bigl[a\) , \( 0\) , \( a\) , \( -186\) , \( 946\bigr] \)
6084.2-e3	\( \bigl[a\) , \( 0\) , \( a\) , \( -36\) , \( -80\bigr] \)
6084.2-e4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -733\) , \( -7888\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph