Elliptic curve isogeny class 2304.3-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-2304.3-b
• Conductor: 2304.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 2304.3-b over \(\Q(\sqrt{-2}) \)

Isogeny class 2304.3-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2304.3-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a - 1\) , \( 0\bigr] \)
2304.3-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 1\) , \( 0\bigr] \)
2304.3-b3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 22 a + 11\) , \( -14 a - 70\bigr] \)
2304.3-b4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 22 a + 11\) , \( 14 a + 70\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph