Elliptic curve isogeny class 387.2-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-387.2-b
• Conductor: 387.2
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 387.2-b over \(\Q(\sqrt{-2}) \)

Isogeny class 387.2-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
387.2-b1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 4 a - 11\) , \( 10 a - 7\bigr] \)
387.2-b2	\( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -9\) , \( a\bigr] \)
387.2-b3	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 20 a + 35\) , \( -63 a + 97\bigr] \)