Elliptic curve isogeny class 44217.6-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-44217.6-b
• Conductor: 44217.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 44217.6-b over \(\Q(\sqrt{-2}) \)

Isogeny class 44217.6-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
44217.6-b1	\( \bigl[1\) , \( 0\) , \( a\) , \( -17 a + 26186\) , \( 1153284 a + 4369\bigr] \)
44217.6-b2	\( \bigl[1\) , \( 0\) , \( a\) , \( -17 a + 1621\) , \( 18381 a - 544\bigr] \)
44217.6-b3	\( \bigl[1\) , \( 0\) , \( a\) , \( 1903 a + 16\) , \( 63222 a + 70787\bigr] \)
44217.6-b4	\( \bigl[1\) , \( 0\) , \( a\) , \( -137 a + 186\) , \( -60 a - 1825\bigr] \)

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