Elliptic curve isogeny class 2304.1-j over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-2304.1-j
• Conductor: 2304.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2304.1-j over \(\Q(\sqrt{2}) \)

Isogeny class 2304.1-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2304.1-j1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a - 4\) , \( -18 a - 26\bigr] \)
2304.1-j2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -24 a - 64\) , \( 36 a - 44\bigr] \)
2304.1-j3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -24 a - 34\) , \( -72 a - 104\bigr] \)
2304.1-j4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 24 a - 64\) , \( -36 a - 44\bigr] \)

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