Elliptic curve isogeny class 35721.4-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-35721.4-b
• Conductor: 35721.4
• Rank: \( 2 \)

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

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

Elliptic curves in class 35721.4-b over \(\Q(\sqrt{-2}) \)

Isogeny class 35721.4-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
35721.4-b1	\( \bigl[0\) , \( 0\) , \( 1\) , \( -54\) , \( -88\bigr] \)
35721.4-b2	\( \bigl[0\) , \( 0\) , \( 1\) , \( -24\) , \( 45\bigr] \)
35721.4-b3	\( \bigl[0\) , \( 0\) , \( 1\) , \( -3834\) , \( -91375\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph