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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-2304.2-g
• Conductor: 2304.2
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
2304.2-g1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -50 a + 14\) , \( 72 a - 198\bigr] \)
2304.2-g2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 50 a + 14\) , \( -72 a - 198\bigr] \)
2304.2-g3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -6\) , \( -18\bigr] \)
2304.2-g4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -35\) , \( 69\bigr] \)

Rank

Rank: \( 1 \)

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