Elliptic curve isogeny class 11858.2-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-11858.2-c
• Conductor: 11858.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 11858.2-c over \(\Q(\sqrt{-2}) \)

Isogeny class 11858.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
11858.2-c1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -4\) , \( -89\bigr] \)
11858.2-c2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -604\) , \( 2343\bigr] \)
11858.2-c3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -324\) , \( -2137\bigr] \)
11858.2-c4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -5164\) , \( -141529\bigr] \)

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