Elliptic curve isogeny class 2304.2-h over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-2304.2-h
• Number of curves: 4
• Conductor: 2304.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

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

Elliptic curves in class 2304.2-h over \(\Q(\sqrt{-2}) \)

Isogeny class 2304.2-h contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2304.2-h1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 10 a + 22\) , \( -20 a + 46\bigr] \)
2304.2-h2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -10 a + 22\) , \( 20 a + 46\bigr] \)
2304.2-h3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 2\) , \( 2\bigr] \)
2304.2-h4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -3\) , \( -3\bigr] \)