Elliptic curve isogeny class 4608.1-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-4608.1-a
• Conductor: 4608.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4608.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 4608.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4608.1-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a + 26\) , \( 36 a + 16\bigr] \)
4608.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( a + 1\) , \( a + 2\bigr] \)
4608.1-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 19\) , \( 8 a + 30\bigr] \)
4608.1-a4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 26 a + 11\) , \( 22 a + 86\bigr] \)

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