Elliptic curve isogeny class 41616.4-f over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.4-f
• Conductor: 41616.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 41616.4-f over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.4-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
41616.4-f1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -10 a + 50\) , \( 64 a - 53\bigr] \)
41616.4-f2	\( \bigl[0\) , \( a\) , \( 0\) , \( 14 a - 50\) , \( -62 a + 23\bigr] \)
41616.4-f3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -175 a + 425\) , \( -1832 a - 3074\bigr] \)
41616.4-f4	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -45 a + 655\) , \( 4776 a + 614\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph