Elliptic curve isogeny class 9801.8-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-9801.8-e
• Conductor: 9801.8
• Rank: \( 1 \)

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

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

Elliptic curves in class 9801.8-e over \(\Q(\sqrt{-2}) \)

Isogeny class 9801.8-e contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
9801.8-e1	\( \bigl[0\) , \( 0\) , \( 1\) , \( -70383\) , \( 7187035\bigr] \)
9801.8-e2	\( \bigl[0\) , \( 0\) , \( 1\) , \( -93\) , \( 625\bigr] \)
9801.8-e3	\( \bigl[0\) , \( 0\) , \( 1\) , \( -3\) , \( -5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph